The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 270270 days and a standard deviation of 1111 days. (a) What is the minimum pregnancy length that can be in the top 88% of pregnancy lengths? (b) What is the maximum pregnancy length that can be in the bottom 33% of pregnancy lengths? (a) The minimum pregnancy length is nothing days. (Round to one decimal place as needed.) (b) The maximum pregnancy length is nothing days.

a) The minimum pregnancy length is 27.1 days.

b) The maximum pregnancy length is 265.2 days.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

(a) What is the minimum pregnancy length that can be in the top 88% of pregnancy lengths?

This is the value of X when Z has a pvalue of 1-0.88 = 0.12. So it is X when Z = -1.175.

The minimum pregnancy length is 27.1 days.

(b) What is the maximum pregnancy length that can be in the bottom 33% of pregnancy lengths?

This is the value of Z when Z has a pvalue of 0.33. So it is X when Z = -0.44.

The maximum pregnancy length is 265.2 days.

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