Question

A simple random sample of size nequals 81 is obtained from a population with mu equals 81 and sigma equals 18 . ?(a) Describe the sampling distribution of x overbar . ?(b) What is Upper P left parenthesis x overbar greater than 84.1 right parenthesis ?? ?(c) What is Upper P left parenthesis x overbar less than or equals 76.2 right parenthesis ?? ?(d) What is Upper P left parenthesis 79.3 less than x overbar less than 84.6 right parenthesis ?? ?(a) Choose the correct description of the shape of the sampling distribution of x overbar . 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 x overbar . mu Subscript x overbar equals sigma Subscript x overbar equals

Answer 1

Answer:

NOrmal distribution

Step-by-step explanation:

As per central limit theorem sample mean follows a normal distribution for large samples drawn at random.

a) X bar follows a normal distribution with mean = 81 and std error = $\frac{\sigma}{\sqrt{n} } =2$

b) $P(X>84.1) = P(Z>\frac{84.1-81}{2} \\=P(Z>1.55)\\= 0.5-0.4394\\\\=0.0606$

c) $P(X\leq 76.2)\\= P(Z\leq \frac{76.2-81}{2} =P(Z\leq2.4)\\= 0.5-0.4793\\=0.0207$

Symmetrical

B. The distribution is approximately normal.