Q. 1.4 - 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.

 Find the probability that the mean pregnancy length for the women in the sample exceeds $270$ davs, Show your work.

Step-by-Step Solution

Answer

The probability is $0.2709.$

Step1: Given Information

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

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

Sample size$\left(n\right)=6$

Step2: Explanation

The probability that the mean pregnancy length for the women is above $270$days can be calculated as:

$$\begin{gathered} P(\overline{x}>270)=P\left(\frac{\overline{x}-\mu }{\frac{\sigma }{\sqrt{n}}}>\frac{270-\mu }{\frac{\sigma }{\sqrt{n}}}\right) \\ =P\left(Z>\frac{270-266}{\frac{16}{\sqrt{6}}}\right) \\ =P(Z>0.61) \\ =0.2709 \end{gathered}$$