Hi! I hope u can help but I least quickly if possible :D

Answer:

The probability of rolling an odd number or a two on a six-sided die is 1/2 + 1/6 = 2/3. This means that if you roll a six-sided die 300 times, you can expect to roll an odd number or a two approximately 200 times

Step-by-step explanation:

Answer: 400 TIMES

Step-by-step explanation:

1/6 +1/2

4/6

2/3

The tangent point of line 2x+3y=-20 is (-7, -1).

To find the point of tangency, determine the intersection point of the line 2x + 3y = -20 and the circle centered at (-3, 4).

The point of tangency will lie on the line that is perpendicular to the tangent line and passes through the center of the circle.

The slope of the given line is -2/3, so the slope of the line that is perpendicular to it is 3/2:

y - 4 = (3/2)(x + 3)

y - 4 = (3/2)x + 9/2

y = (3/2)x + 17/2

Substitute this expression for y into the equation of the tangent line and solve for x:

2x + 3y = -20

2x + 3[(3/2)x + 17/2] = -20

2x + (9/2)x + 51/2 = -20

(13/2)x = -91/2

x = -7

Substituting this value of x into the equation of the line:

y = (3/2)x + 17/2 = (3/2)(-7) + 17/2 = -1

Therefore, the point of tangency is (-7, -1).

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The volume of a rectangle is 9 [tex]units^3[/tex] if L = 1.2, W = 3, H = 2.5

The rectangular prism is a three-dimensional geometric figure. The product of all three dimensions is equal to its volume. If the dimensions are in the form of expression, then we have to multiply those three expressions and simplify it to find the expression for the volume of the rectangular prism.

We are given the dimensions of a rectangular prism, where the length is l = 1.2 the width is w = 3 and the height is , h = 2.5 We are asked to find the expression that represents the volume of the prism. Using the formula for the volume of a rectangular prism, we have

V = l × w × h

Plug all the values in above formula

V = 1.2 × 3 × 2.5

V = 9 [tex]units^3[/tex]

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The overinvolvement ratio for high study levels in high test scores over low test scores is 0.833 (rounded to three decimal places as requested).

The overinvolvement ratio is a measure of the association between two variables. In this case, we want to measure the association between high study levels and high test scores.

Let's define the following events:

A: the event that a student studies more than 25 hours per week.

B: the event that a student received high scores on tests.

Using this notation, we know that:

P(A|B) = 0.5 (50% of students who received high scores study more than 25 hours per week)

P(A|~B) = 0.7 (70% of students who received low scores study more than 25 hours per week)

The overinvolvement ratio is defined as the ratio of the conditional probabilities:

overinvolvement ratio = P(B|A) / P(B|~A)

We can use Bayes' theorem to calculate these probabilities:

P(B|A) = P(A|B) * P(B) / P(A)

P(B|~A) = P(~A|B) * P(B) / P(~A)

where P(B) is the probability that a student received high scores on tests, which we don't know.

However, we can use the law of total probability to calculate it:

P(B) = P(B|A) * P(A) + P(B|~A) * P(~A)

Substituting the values we know:

P(B) = (0.5 * 0.5) + (0.3 * 0.5) = 0.4

Now we can calculate the overinvolvement ratio:

overinvolvement ratio = P(B|A) / P(B|~A)

overinvolvement ratio = (0.5 * 0.4) / (0.3 * 0.6)

overinvolvement ratio = 0.833.

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Answer:

Area is 102 meters squared

Step-by-step explanation:

A = a+b/2 (h)

a = 7

b = 10

h = 12

A = 7+10/2 (12)

A = 17/2 (12)

A = 17/2 x 12/1

A = 204/2

A = 102

The integral test can be used to determine the convergence or divergence of a series of positive terms. To apply the test, you must first find an integral that is equivalent to the series. If the integral converges, then the series also converges.

If the integral diverges, then the series also diverges. Specifically, if the integral is finite (i.e. converges), then the series converges. If the integral is infinite (i.e. diverges), then the series diverges. Keep in mind that the integral test only applies to series with positive terms.
Hi! To determine if a series converges or diverges using the integral test, you need to consider these terms: improper integral, continuous function, positive, and decreasing function.

If the function f(x) is continuous, positive, and decreasing on the interval [1, ∞), you can use the integral test. Evaluate the improper integral ∫f(x)dx from 1 to ∞. If the integral converges, the series also converges. If the integral diverges, the series diverges as well.

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The general solution to the non-homogeneous equation is

[tex](c_1 + 3) e^{t/2} + c_2 e^{-t/2}[/tex]

We have,

To solve the differential equation 4y" - y = 8e^{t/2}/2 + e^{t/2}, we first need to find the complementary solution by solving the homogeneous equation 4y" - y = 0.

The characteristic equation is 4r² - 1 = 0, which has roots r = ±1/2. Therefore, the complementary solution is:

y_c(t) = c_1 e^{t/2} + c_2 e^({-t/2}

where c_1 and c_2 are constants determined by the initial or boundary conditions.

Next, we need to find a particular solution to the non-homogeneous equation. Since the right-hand side contains e^{t/2}, we try a particular solution of the form:

y_p(t) = A e^{t/2}

where A is a constant to be determined.

Taking the first and second derivatives of y_p(t), we get:

y_p'(t) = A/2 e^{t/2}

y_p''(t) = A/4 e^{t/2}

Substituting these into the original differential equation, we get:

4(A/4 e^{t/2}) - A e^{t/2} = 8e^{t/2}/2 + e^{t/2}

Simplifying, we get:

A = 3

Therefore,

The particular solution is:

y_p(t) = 3 e^{t/2}

The general solution to the non-homogeneous equation is then:

y(t) = y_c(t) + y_p(t)

= c_1 e^{t/2} + c_2 e^{-t/2} + 3 e^{t/2}

= (c_1 + 3) e^{t/2} + c_2 e^{-t/2}

where c_1 and c_2 are constants determined by the initial or boundary conditions.

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Based on the information, these manufacturers have different mean times.

The following can be deduced based on the information:

sum of sq;treatment= 394.67

sum of sq; error= 44.00

mean sq;treatment= 197.33

mean square; error= 4.89

test statistic = 40.36

Pvalue is less than 0.01.

Fisher's (LSD) =(t)*(sp*√(1/ni+1/nj) =  3.54

since sample mean difference between 1 and 3 is greater than 3.54:

Based on this, the manufacturers have different mean times.

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The probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication is :

(e) 0.90

To find the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication, you can use the following formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

where:
P(A ∪ B) is the probability of taking either blood pressure-lowering (A) or cholesterol-lowering (B) medication,
P(A) is the probability of taking blood pressure-lowering medication,
P(B) is the probability of taking cholesterol-lowering medication, and
P(A ∩ B) is the probability of taking both medications.

From the survey, we have the following probabilities:
P(A) = 0.52 (52% take blood pressure-lowering medication)
P(B) = 0.43 (43% take cholesterol-lowering medication)
P(A ∩ B) = 0.05 (5% take both medications)

Now, substitute the values into the formula:

P(A ∪ B) = 0.52 + 0.43 - 0.05
P(A ∪ B) = 0.90

Therefore, the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication is 0.90, or 90%.

The correct answer is:

(e.) 0.90.

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Answer:

C!

Step-by-step explanation:

i took this test!

<3

Answer:

c.3

Step-by-step explanation

if h =3 then it would be 3 x (4-3)

4-3=1

3x1=3

so there for 3x(4-3)=3

parantheses

exponents

multiplication

division

addition

subtraction

The value of k for which P(Z ≤ k) = 0.258 is k = 0.65.

To find the value of k for which P(Z ≤ k) = 0.258, we need to use a standard normal distribution table or a calculator that can compute the inverse of the standard normal cumulative distribution function.

Using a standard normal distribution table, we can find the closest probability value to 0.258, which is 0.2580. Then, we look for the corresponding z-score in the table, which is approximately 0.65. Therefore, the value of k for which P(Z ≤ k) = 0.258 is k = 0.65.

Alternatively, we can use a calculator that can compute the inverse of the standard normal cumulative distribution function, such as the NORMSINV function in Excel or the invNorm function in a graphing calculator. Using this method, we can input the probability value of 0.258 and the calculator will return the corresponding z-score, which is approximately 0.65.

It's important to note that the value of k represents the cutoff point below which the cumulative probability is 0.258. In other words, P(Z ≤ k) = 0.258 means that there is a 25.8% probability that a random observation from a standard normal distribution is less than or equal to k. The remaining probability of 1 - 0.258 = 0.742 is the area to the right of k, which represents the probability that a random observation is greater than k.

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a) The length of the median BE = √(10)

b) The length of the altitude BH = √(5)

c) The size of the angle ABC = 135.0°

d) The area of the triangle A = √(50)

e) The perimeter of the triangle = √(10) + √60

To solve this problem, we can begin by finding the coordinates of the vertices of the triangle by solving the system of equations formed by the given lines.

AB: 2x + 6y + 2 = 0

BC: 3x + 2y – 10 = 0

CA: 5x – 2y + 10 = 0

Solving for x and y, we get:

A(-2,2), B(-1,-1), C(2,-3)

a) To find the length of the median BE, we first need to find the midpoint of AC. Using the midpoint formula, we get D(0,-0.5). Then, we can use the distance formula to find the length of BE:

BE = √(((-1-2)² + (-1-3)²)/4) = √(10)

b) To find the length of the altitude BH, we need to find the equation of the line perpendicular to AB that passes through B. The slope of AB is -1/3, so the slope of the perpendicular line is 3. Using the point-slope form of the equation, we get:

y + 1 = 3(x + 1)

Solving for the point where this line intersects BC, we get H(-3,-8). Then, we can use the distance formula to find the length of BH:

BH = √(((-3-1)² + (-8-1)²)/10) = √(5)

c) To find the size of the angle ABC, we can use the dot product formula:

cos(ABC) = (AB dot BC) / (|AB| * |BC|)

We can find AB and BC using the distance formula, and then use the dot product formula to find cos(ABC), and then take the inverse cosine to find the angle ABC:

AB = √((-1-2)² + (-1-2)²) = √(10)

BC = √((-1-2)² + (-1-3)²) = √(15)

cos(ABC) = (-7/√150) / (√10 * √15) = -7/10

ABC = cos^-1(-7/10) = 135.0°

d) To find the area of the triangle, we can use the formula A = 1/2 * base * height, where the base can be any side of the triangle, and the height is the length of the altitude drawn to that side. Let's use AB as the base, and BH as the height:

A = 1/2 * √(10) * √(5) = √(50)

e) To find the perimeter of the triangle, we simply add up the lengths of all three sides:

AB + BC + CA = √(10) + √(15) + 2√10 = √(10) + √60

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The probability that the random variable X has a value greater than 5.3 is 0.47 or 47%.

Since X is uniformly distributed between 0 and 10 with a density of 0.1, we know that the probability density function (PDF) is:

f(x) = 0.1,  0 < x < 10

To find the probability that X is greater than 5.3, we need to integrate the PDF from 5.3 to 10:

P(X > 5.3) = ∫[5.3,10] f(x) dx

          = ∫[5.3,10] 0.1 dx

          = 0.1 * ∫[5.3,10] dx

          = 0.1 * [x]_[5.3,10]

          = 0.1 * (10 - 5.3)

          = 0.47

Therefore, the probability that the random variable X has a value greater than 5.3 is 0.47 or 47%.

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V(X) = 10.00

Explanation: A fair 6-sided dice are rolled a number of times, and let X is the number of sixes. The mean value of X is given as 2. To calculate the variance V(X), we'll use the formula for the variance of a binomial distribution:

V(X) = np(1-p),

where n is the number of trials and p is the probability of success (rolling a six).
Since the mean value of X is 2, we can write it as np = 2. The probability of rolling a six on a fair 6-sided dice is p = 1/6. We can solve for n using the mean value:

n(1/6) = 2
n = 12

Now that we know n, we can calculate the variance:

V(X) = np(1-p) = 12(1/6)(1 - 1/6) = 12(1/6)(5/6) = 10

So, the variance V(X) is 10.00 (rounded to 2 decimal places).

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On solving the provided query we have The test statistic (-2.5594) falls in  equation the rejection zone since it is less than the threshold value (-2.009).

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

a. The average hourly wage is equal to $22 under the null hypothesis, whereas it is not $22 under the alternative hypothesis.

A = $22 is the null hypothesis (H0).

Additional Hypothesis (Ha): $22

b. The test statistic's value can be determined as follows:

t = sqrt(sample size) / (population standard deviation / hypothesised mean) / (sample mean - hypothesised mean)

t = (20.2106 - 22) / (6 / sqrt(50))

t = -2.5594

c. The critical value with 49 degrees of freedom and a 5% significance level is 2.009.

d. The test statistic (-2.5594) falls in the rejection zone since it is less than the threshold value (-2.009).

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The probability of answering between 70 and 80 questions, inclusive, is 0.0676

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

P(70 ≤ X ≤ 80) = P(X = 70) + P(X = 71) + ... + P(X = 80)

Using the binomial probability formula, we get:

[tex]P(X = k) = (n choose k) * p^k * (1-p)^{(n-k)}[/tex]

where (n choose k) is the binomial coefficient, which can be calculated as:

(n choose k) = n! / (k! * (n-k)!)

Using a calculator or software, we can find:

P(70 ≤ X ≤ 80) = 0.0676

Therefore, the probability of answering between 70 and 80 questions, inclusive, is 0.0676 (rounded to four decimal places).

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The point-biserial correlation is specifically designed for this type of analysis and is used to determine the degree of association between a binary variable and a continuous variable.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

The most appropriate type of correlation for the psychologist to use in this scenario would be a point-biserial correlation. This is because the psychologist wants to measure the relationship between a dichotomous variable (whether parents were divorced or not) and a continuous variable (relationship satisfaction scores).

The point-biserial correlation is specifically designed for this type of analysis and is used to determine the degree of association between a binary variable and a continuous variable.

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Answer:

18

Step-by-step explanation:

(1 1/2 ✖ 2 ✖ 3) ➗1/2

Answer: 18

Step-by-step explanation:

first find the volume 1.5x3x2=9

then you take 9 and divide it by 0.5

9/0.5 is 18

1. You can write the sample space for flipping a coin twice as HH, HT, TH, TT, where H stands for heads and T for tails.

2) The probability of flipping 2 heads can be calculated by multiplying the probabilities of getting a head on the first flip and the second flip:

P(2H) = P(H) x P(H) = 0.65 x 0.65 = 0.4225

Consequently, the likelihood of flipping two heads is 0.4225, rounded to four decimal place

3) We can use the following calculation to determine the likelihood of flipping exactly one head:

P(1H) = P(HT or TH) = P(HT) + P(TH)

P(HT) = P(H) x P(T) = 0.65 x 0.35 = 0.2275

P(TH) = P(T) x P(H) = 0.35 x 0.65 = 0.2275

P(1H) = 0.2275 + 0.2275 = 0.455

Consequently, the likelihood of flipping two heads is 0.4225, rounded to four decimal places.

4) You may calculate the likelihood of flipping at least one head by deducting the likelihood of flipping no heads from one:

P(at least 1H) = 1 - P(0H)

To find P(0H), we can use the formula:

P(0H) = P(TT) = P(T) x P(T) = 0.35 x 0.35 = 0.1225

So, P(at least 1H) = 1 - 0.1225 = 0.8775

Therefore, the probability of flipping at least 1 head is 0.8775, rounded to 4 decimal places.

5)  You may calculate the likelihood of receiving no heads by multiplying the chances of getting a tail on the first and second flips:

P(0H) = P(T) x P(T) = 0.35 x 0.35 = 0.1225

So, the probability of flipping no heads is 0.1225, rounded to 4 decimal places.

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(a) To determine whether the data presents sufficient evidence to verify the manufacturer's claim, we can perform a one-sample t-test. The null and alternative hypotheses are:

H0: µ >= 80% (the mean potency of the antibiotic is at least 80%)

Ha: µ < 80% (the mean potency of the antibiotic is less than 80%)

The test statistic is calculated as:

t = (X - µ) / (s / sqrt(n))

where X is the sample mean, µ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values from the problem, we get:

t = (79.7 - 80) / (0.2 / sqrt(100)) = -2.5

Using a t-distribution table with 99 degrees of freedom and a significance level of 0.05, we find the critical value to be -1.660.

Since our calculated t-value (-2.5) is less than the critical value (-1.660), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean potency of the antibiotic is less than 80%.

(b) The p-value for this test is the probability of obtaining a t-value as extreme as -2.5 (or more extreme) assuming that the null hypothesis is true. This is a one-tailed test, so the p-value is:

p-value = P(t < -2.5) = 0.007

Therefore, the p-value for this test is 0.007. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean potency of the antibiotic is less than 80%.

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The value of p could be either 0.2846 or 0.7154.

To find the value of p, we need to use the formula for the probability of k successes in a multinomial distribution:

P(k1,k2,...,kn) = n!/(k1!k2!...kn!) * p1k1 * p2k2 * ... * pn^kn

where n is the number of trials, k1,k2,...,kn are the number of successes in each category, and p1,p2,...,pn are the probabilities of success in each category.

Since we are given that the probability of five successes out of ten trials is 0.2007, we can set k1=5, k2=0, ..., kn=0, and solve for p:

0.2007 = 10!/(5!0!...0!) * p5 * (1-p)5

0.2007 = 252 * p5 * (1-p)5

0.000795238 = p5 * (1-p)5

Taking the fifth root of both sides, we get:

0.5707 = p * (1-p)

Solving for p using the quadratic formula, we get:

p = 0.2846 or p = 0.7154

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1.Here, a is the value of the random variable Z that corresponds to the given probability of 0.0228. 2. If Z is the standard normal random variable, then P(1.00 < Z < 2.00) = 0.1359.

1. If Z is the standard normal random variable and P(Z > a) = 0.0228, then the value of a is approximately 2.00.

This means that there is a 2.28% probability that a random value from the standard normal distribution will be greater than 2.00.

2. If Z is the standard normal random variable, then P(1.00 < Z < 2.00) is the probability of the variable falling between 1.00 and 2.00.

To find this, you can subtract the cumulative probability for Z=1.00 from the cumulative probability for Z=2.00.

This value is approximately 0.1359, meaning there is a 13.59% probability that a random value from the standard normal distribution will fall between 1.00 and 2.00.

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a) Sample size is A. 637.

b) The sample size would decrease.

a) To determine the sample size needed to estimate the mean surgical wait time with a margin of error of 0.8 days and a 98% confidence level, we can use the formula:

n = [tex](\frac{zs}{E})^{2}[/tex]

where:

z = the z-score corresponding to the desired confidence level, which is 2.33 for a 98% confidence level

s = the population standard deviation, which is 10.3 days

E = the desired margin of error, which is 0.8 days

Substituting the values into the formula, we get:

n = [tex](\frac{2.33*10.3}{0.8} )^{2}[/tex] ≈ 637

Therefore, the sample size needed is 637, which corresponds to option A.

b) If the level of confidence was decreased to 95%, the sample size required would decrease. This is because a lower confidence level requires a smaller margin of error, which means we can achieve it with a smaller sample size. However, the exact sample size required would depend on the new desired margin of error and the updated level of confidence.

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The image of the trapezoid after a dilation with a scale factor of 12 will have new coordinates K'(-72, 24), L' = (24, 24), M'(48, -48), N'(-96, -48).

A trapezoid is a four-sided polygon that has two parallel sides and two non-parallel sides, which are called the bases and legs respectively. The height of a trapezoid is the shortest distance between the two bases. To find the area of a trapezoid, you can use the formula A = [tex]\frac{ (b1 + b2)h}{2}[/tex] , where b1 and b2 are the lengths of the two bases and h is the height.

To find the image of the trapezoid after a dilation with a scale factor of 12, we need to multiply the coordinates of each vertex by 12.

The coordinates of the vertices are:

K(-6, 2)

L(2, 2)

M(4, -4)

N(-8, -4)

Multiplying each coordinate by 12, we get:

K': (12 × -6, 12 × 2) = (-72, 24)

L': (12 × 2, 12 × 2) = (24, 24)

M': (12 × 4, 12 × -4) = (48, -48)

N': (12 × -8, 12 × -4) = (-96, -48)

Plotting this we get the following graphs.

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The value of c is 0.63 such that  P ( z ≤ c) = 0.7357 where Z follows standard normal distribution using z- score table.

The values that range from 0 to 1 in a z-table are referred to as the probabilities of various z-scores. To calculate the z- score with given probability we need to identify the row and the column the probability belongs to in the z- score table as they indicate the z- score.

Z is said to follow standard normal distribution.

Using a z- score table we can observe that probability 0.7357 lies in the column 0.03 and the row 0.6.

Therefore, summing up the row and column value of the probability we get the z- score.

That is, z- score = 0.03 + 0.6 = 0.63

Thus P ( z ≤ c) = 0.7357 can be written as,

P ( z ≤ 0.63) = 0.7357

Therefore, c = 0.63 (rounded up to two decimal places)

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The given question is incomplete, the complete question is

"Let Z be a standard normal random variable. Determine the value of c such that P(Z ≤ c) = 0.7357.

Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places."

As mining representative, the actions which can be taken to address citizen's concerns are through:

The primary concerns of the people would be the potential environmental impact of the mining activity, so, it is important to engage in open communication with them to address these concerns and inform them about steps being taken to minimize environmental impacts.

This can involve providing regular updates on environmental monitoring and management plans as well as holding public meetings to address concerns and answer questions.

The company will also implement measures to mitigate environmental impacts like using best available technologies to reduce emissions and waste, reclaiming and restoring mined land and minimizing water usage.

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y = (1/4)e^(3x) + C/e^x this is the general solution to the given differential equation. It does not match any of the given options A through E.

To find the general solution to the differential equation dy/dx = e^(3x-y), we first rewrite it as a first-order linear differential equation. Divide both sides by e^(-y) to obtain:
dy/dx + y = e^(3x).
Now, we can solve this using an integrating factor. The integrating factor is given by the exponential of the integral of the coefficient of y with respect to x:
IF = e^(∫1 dx) = e^x.
Multiply the entire equation by the integrating factor:
(e^x)dy/dx + (e^x)y = e^(3x)e^x.
Now, the left side of the equation is the derivative of the product of y and the integrating factor (e^x):
d/dx(ye^x) = e^(4x).
Integrate both sides with respect to x:
∫d(ye^x) = ∫e^(4x) dx.
ye^x = (1/4)e^(4x) + C.
Finally, isolate y by dividing both sides by e^x:
y = (1/4)e^(3x) + C/e^x.
This is the general solution to the given differential equation. It does not match any of the given options A through E.

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The correct order in greatest to least is A) 5, π, [tex]\sqrt{2}[/tex], 0.76, -2, 1/2.

Ordering the numbers from greatest to least: 5, π, √2, 0.76, -2, ½

To order the numbers from greatest to least we need to check all the numbers given and then we specify the smallest and largest value corresponding to the given numbers. Also ordering can be done in ascending order from least to greatest value which is increasing order.

If we want to specify the descending order for the given numbers the order of ascending will be totally reversed. Then we will get the numbers from greatest to the least in order which means decreasing order.

Therefore, the answer is (A) 5, π, [tex]\sqrt{2}[/tex], 0.76, -2, 1/2.

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The percentage of scores that are between 42 and 58 on this standardized test is calculated to be 95.44%

To find the percent of scores between 42 and 58, we need to first calculate the z-scores for each of these values using the formula:
z = (score - mean) / standard deviation
For a score of 42:
z = (42 - 50) / 4 = -2
For a score of 58:
z = (58 - 50) / 4 = 2
Next, we can use a z-table to find the area under the normal distribution curve between these two z-scores. Since the table gives us the area to the left of a z-score, we need to subtract the area to the left of -2 from the area to the left of 2:
area between -2 and 2 = area to the left of 2 - area to the left of -2
= 0.9772 - 0.0228
= 0.9544
So approximately 95.44% of scores are between 42 and 58 on this standardized test.

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