Question

I need help with this 3- part question, part A is completed

Answer 1

Since we want the sampling distribution of X, then we have the following:

`\begin{gathered} n=25 \\ \mu_{\bar{X}}=\mu=73 \\ \sigma_{\bar{X}}=\frac{\sigma}{\sqrt[]{n}}=\frac{12.5}{\sqrt[]{25}}=2.5 \end{gathered}`

then, we can calculate the probability by normalizing the variable X hat:

`P(\bar{X}<77)=P(\frac{\bar{X}-\mu_X}{\sigma_X}<(77-73)/(2.5))=P(Z<1.6)=0.9452`

therefore, the probability is 0.9452