Question

The mean length of a human pregnancy is 270 ​days, with a standard deviation of 99 days. Use the empirical rule to determine the percentage of women whose pregnancies are between 252 and 288 days.​ (Assume the data set has a​ bell-shaped distribution.)

A. ​50%

B. 68​%

C. 95​%

D. 99.7%

Answer 1

Corrrect answer: C) 95%

Note: There is on mistake in question Standard deviation should be = 9 (maybe misprinting, so i solved the problem with Standard deviation=9)

Explanation:

By assuming the distrbution is normally ditributed, the required probability is obtained by first converting normal distribution to standard normal distribution then the probability is obtained using the standard normal distribution table,

The required probability is,

Now the normally distributed random variable X is converted to standard normal as shown below,

The equation can be written as,

This probability is obtained using the standard normal distribution table for z = -2 and z = 2,

Hence the are 95% women are have pregnency days between 252 and 288.