The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 267 days and standard deviation 19 days. Use the 68-95-99.7 rule to answer the following questions.

(a) Between what values do the lengths of the middle 95% of all pregnancies fall?anddays

(b) How short are the shortest 2.5% of all pregnancies?days or less

c) How long do the longest 2.5% of pregnancies last?days or more

a) 229 and 305 days

b) 229 days or less

c) 305 days or more

Step-by-step explanation:

The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 267

Standard deviation = 19

(a) Between what values do the lengths of the middle 95% of all pregnancies fall?anddays

By the Empirical rule, 95% of all pregnancies fall within 2 standard deviations of the mean.

So

267 - 2*19 = 229 days

to

267 + 2*19 = 305 days

(b) How short are the shortest 2.5% of all pregnancies?days or less

95% of all pregnancies fall within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. Since the distribution is symmetric, 2.5% is more than 2 standard deviations below the mean(shortest 2.5%) and 2.5% is more than 2 standard deviations above the mean(longest 2.5%). So

267 - 2*19 = 229 days

c) How long do the longest 2.5% of pregnancies last?days or more

Explanation in b)

267 + 2*19 = 305 days