(Solved): Suppose a simple random sample of size n=49 is obtained from a population that is skewed right with ...

Suppose a simple random sample of size $n=49$ is obtained from a population that is skewed right with $\mu =84$ and $\sigma =21$. (a) Describe the sampling distribution of $\bar{x}$. (b) What is $P(\bar{x}>88.65)$ ? (c) What is $P(x\le 76.8)$ ? (d) What is $P(81<\bar{x}<88.65)$ ? (a) Choose the correct description of the shape of the sampling distribution of $\bar{x}$. A. The distribution is skewed right. B. The distribution is skewed left. C. The distribution is uniform. D. The distribution is approximately normal. E. The shape of the distribution is unknown. Find the mean and standard deviation of the sampling distribution of $\bar{x}$. $\begin{array}{l}{\mu }_{\bar{x}}=\\ {\sigma }_{\bar{x}}=\end{array}$ (Type integers or decimals. Do not round.) (b) $P(\bar{x}>88.65)=$ (Round to four decimal places as needed.) (c) $P(\bar{x}\le 76.8)=$ (Round to four decimal places as needed.) (d) $P(81<\bar{x}<88.65)=$ (Round to four decimal places as needed.)