According to a study conducted in one city, $39 \%$ of adults in the city have credit card debts of more than $\$ 2000$. A simple random sample of $n = 100$ adults is obtained from the city. Describe the sampling distribution of $p$, the sample proportion of adults who have credit card debts of more than $\$ 2000$.
A) Approximately normal; $\mu _ { \mathrm { p } } = 0.39 , \sigma _ { \mathrm { p } } = 0.049$
B) Exactly normal; $\mu _ { p } = 0.39 , \sigma p = 0.049$
C) Approximately normal; $\mu _ { \mathrm { p } } = 0.39 , \sigma _ { \mathrm { p } } = 0.0024$
D) Binomial; $\mu _ { \mathrm { p } } = 39 , \sigma _ { \mathrm { p } } = 4.88$ 2 Compute probabilities of a sample proportion.

Question

Quizplus · Accepted Answer

The sampling distribution of $p$ is approximately normal due to the Central Limit Theorem, given a large enough sample size. The mean of the sampling distribution, $\mu_p$, equals the population proportion, which is 0.39. The standard deviation of the sampling distribution, $\sigma_p$, is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, which equals $\sqrt{\frac{0.39(1-0.39)}{100}} = 0.049$.

According to a Study Conducted in One City 39%39 \%39% Of Adults in the City Have Credit Card Debts of Of Adults

According to a Study Conducted in One City $39 \%$ Of Adults in the City Have Credit Card Debts of Of Adults