Whales have one of the longest gestation periods of any mammal. According to a website, the mean gestation period for a whale is 15 months. Assume the distribution of gestation periods is Normal with a standard deviation of 1.1
months
a. Find the standard score associated with a gestation period of 13.9 months.
b. Using the Empirical Rule and your answer to part a, what percentage of whale pregnancies will have a gestation period between 13.9 and 15 months?
c. Would it be unusual for a whale to have a gestation period of 19 months? Why or why not?

a. A gestation period of 13.9 months has a standard score of -1.36.

b. Approximately 99.7% will fall within three standard deviations of the mean.

c. A gestation period of 19 months is very unlikely to occur in a normal distribution, and it would be considered unusual.

What is standard score?

a. To find the standard score associated with a gestation period of 13.9 months, we use the formula:

z = (x - μ) / σ

where x is the gestation period, μ is the mean gestation period, and σ is the standard deviation. Plugging in the values given, we get:

z = (13.9 - 15) / 1.1 = -1.36

Therefore, a gestation period of 13.9 months has a standard score of -1.36.

Empirical Rule:

b. Using the Empirical Rule, we know that approximately 68% of the gestation periods will fall within one standard deviation of the mean, approximately 95% will fall within two standard deviations of the mean, and approximately 99.7% will fall within three standard deviations of the mean.

Since we found the standard score in part a, we can use it to calculate the percentage of whale pregnancies that will have a gestation period between 13.9 and 15 months. This gestation period range is within one standard deviation of the mean, so we can say that approximately 68% of whale pregnancies will fall within this range.

What is gestation period?

c. A gestation period of 19 months is more than three standard deviations away from the mean gestation period of 15 months. Using the Empirical Rule, we can say that approximately 99.7% of the gestation periods will fall within three standard deviations of the mean. Therefore, a gestation period of 19 months is very unlikely to occur in a normal distribution, and it would be considered unusual.

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a ___ weather front forms when a warm air mass pushes into a cooler air mass

a) cold
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c) stationary