Q. 1.1 - The Practice of Statistics for AP

Question

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean $266$days and standard deviation $16$days.

1. Find the probability that a randomly chosen pregnant woman has a pregnancy that lasts for more than $270$days. Show your work.

Suppose we choose an$\mathrm{SRS}$ of 6 pregnant women. $\overline{x}=$ the mean pregnancy length for the sample.

Step-by-Step Solution

Answer

 The probability is  0.4013 .

Step1: Given Information

Population mean $\left(\mu \right)=266$

Population standard deviation $\left(\sigma \right)=16$

Step2: Explanation

The probability that a randomly selected woman has a pregnancy that would be above$270$days can be calculated as:

$$\begin{gathered} P(X>270)=P\left(\frac{x-\mu }{\sigma }>\frac{270-\mu }{\sigma }\right) \\ =P\left(Z>\frac{270-266}{16}\right) \\ =P(Z>0.25) \\ =0.4013 \end{gathered}$$