Question

# Suppose *x* has a distribution

with a mean of 90 and a standard deviation of 36. 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---

an approximately normal

a Poisson

an unknown

a geometric

a binomial

a normal

distribution with mean *μ*_{x} =

and standard deviation *σ*_{x} =

.

(b) Find the *z* value corresponding to *x* = 81.

*z* =

(c) Find *P*(*x* < 81).

(Round your answer to four decimal places.)

*P*(*x* < 81) =

(d) Would it be unusual for a random sample of size 64 from the *x* distribution to have a sample mean less than 81? Explain.