Question

Suppose x has a distribution

with a mean of 50 and a standard deviation of 3. Random samples of size n = 36

are drawn.

(a) Describe the x distribution

and compute the mean and standard deviation of the distribution.

has

—Select—

a normal

an approximately normal

a geometric

a binomial

a Poisson

an unknown

distribution with mean μ_x =

and standard deviation σ_x = .

(b) Find the z value corresponding to x = 51.

z =

(Round your answer to four decimal places.)

P(x < 51) =

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 51? Explain.

No, it would not be unusual because more than 5% of all such samples have means less than 51.

Yes, it would be unusual because less than 5% of all such samples have means less than 51.

No, it would not be unusual because less than 5% of all such samples have means less than 51.

Yes, it would be unusual because more than 5% of all such samples have means less than 51.