Question

the lengths of pregnancies are normally distributed with a mean of 265 days and a standard deviation of 30 days. if 144 women are randomly selected, find the probability that they have a mean pregnancy between 265 days and 267 days. a. 0.7881 b. 0.2881 c. 0.2119 d. 0.5517

Explanation:

Step1: Calculate the standard error

The standard error formula is $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$. Given $\sigma = 30$ and $n = 144$, then $\sigma_{\bar{x}}=\frac{30}{\sqrt{144}}=\frac{30}{12}=2.5$.

Step2: Calculate the z - scores

The z - score formula is $z=\frac{\bar{x}-\mu}{\sigma_{\bar{x}}}$.
For $\bar{x}=265$, $z_1=\frac{265 - 265}{2.5}=0$.
For $\bar{x}=267$, $z_2=\frac{267 - 265}{2.5}=\frac{2}{2.5}=0.8$.

Step3: Find the probability

We want $P(0

Answer:

B. 0.2881