1. For a population of qualitative data, P = 63% of the items have a certain characteristic of interest (i.e., success). Suppose a sample of 146 items are randomly chosen, and $\hat{P}$ is the proportion of the sample that have the characteristic of interest.
a. Verify that the probability distribution of $\hat{P}$ is approximately normal.
b. Compute $\mu_{\hat{P}}$.
c. Compute $\sigma_{\hat{P}}$ to two decimal places.
d. Label the idealized probability distribution of $\hat{P}$.
e. Convert $\hat{P} = 0.60$ to a z score.
f. State the meaning of the answer to part (e).
g. Compute $P(\hat{P} > 0.60)$.