Questions: Suppose a simple random sample of size n=36 is obtained from a population that is skewed right with μ=79 and σ=6. (a) Describe the sampling distribution of x̄. (b) What is P(x̄>80.5) ? (c) What is P(x̄ ≤ 77) ? (d) What is P(77.55<x̄<81.4) ? (a) Choose the correct description of the shape of the sampling distribution of x̄. A. The distribution is skewed right. B. The distribution is approximately normal. C. The distribution is skewed left. D. The distribution is uniform. E. The shape of the distribution is unknown. Find the mean and standard deviation of the sampling distribution of x̄. μx̄=□ σx̄=□ (Type integers or decimals. Do not round.) (b) P(x̄>80.5)= □ (Round to four decimal places as needed.) (c) P(x̄ ≤ 77)= □ (Round to four decimal places as needed.) (d) P(77.55<x̄<81.4)= □ (Round to four decimal places as needed.)
Transcript text: Suppose a simple random sample of size $n=36$ is obtained from a population that is skewed right with $\mu=79$ and $\sigma=6$.
(a) Describe the sampling distribution of $\bar{x}$.
(b) What is $P(\bar{x}>80.5)$ ?
(c) What is $P(\bar{x} \leq 77)$ ?
(d) What is $P(77.55<\bar{x}<81.4)$ ?
(a) Choose the correct description of the shape of the sampling distribution of $\overline{\mathrm{x}}$.
A. The distribution is skewed right.
B. The distribution is approximately normal.
C. The distribution is skewed left.
D. The distribution is uniform.
E. The shape of the distribution is unknown.
Find the mean and standard deviation of the sampling distribution of $\bar{x}$.
\[
\begin{array}{l}
\mu_{\bar{x}}=\square \\
\sigma_{\bar{x}}=\square
\end{array}
\]
(Type integers or decimals. Do not round.)
(b) $P(\bar{x}>80.5)=$ $\square$ (Round to four decimal places as needed.)
(c) $P(\bar{x} \leq 77)=$ $\square$ (Round to four decimal places as needed.)
(d) $P(77.55<\bar{x}<81.4)=$ $\square$ (Round to four decimal places as needed.)
Solution
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