Question

Suppose x has a distribution with a mean of 40 and a standard deviation of 20. Random samples of size n = 64 are drawn.

(a) Describe the x bar distribution.

x bar has a normal distribution.

x bar has a geometric distribution.

x bar has an approximately normal distribution.

x bar has a Poisson distribution.

x bar has an unknown distribution.

x bar has a binomial distribution.

Compute the mean and standard deviation of the distribution. (For each answer, enter a number.)

mu sub x bar=

sigma sub x bar =

(b) Find the z value corresponding to x bar = 45. (Enter an exact number.)

z =

(c) Find P(x bar < 45). (Enter a number. Round your answer to four decimal places.)

P(x bar < 45) =

(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 45? Explain.

Yes, it would be unusual because less than 5% of all such samples have means less than 45.

No, it would not be unusual because more than 5% of all such samples have means less than 45.

Yes, it would be unusual because more than 5% of all such samples have means less than 45.

No, it would not be unusual because less than 5% of all such samples have means less than 45.

Answer 1

if x follows ,Then

answer with steps given below