Question

Suppose x has a distribution with a mean of 40 and a standard deviation of 28. Random samples of size n = 64 are drawn.

(a) Describe the x distribution and compute the mean and standard deviation of the distribution.

x has  ---Select---

a binomial

an approximately normal

a normal

a geometric

an unknown

a Poisson distribution

with mean μ_x = ? and standard deviation σ_x =  .?

(b) Find the z value corresponding to x = 33.

z =

c) Find P(x < 33). (Round your answer to four decimal places.)

P(x < 33) =

(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 33? Explain.

No, it would not be unusual because less than 5% of all such samples have means less than 33.

Yes, it would be unusual because more than 5% of all such samples have means less than 33.    

Yes, it would be unusual because less than 5% of all such samples have means less than 33.

No, it would not be unusual because more than 5% of all such samples have means less than 33.

Answer 1

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Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(-2, TRUE)" to find the probability.

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Since the probability is 0.0227 (2.27%) which is less than 0.05 (5%). Hence considered unusual.