Suppose x has a distribution with a mean of 90 and a standard deviation

of 27. Random samples of size n = 36
are drawn.
(a) Describe the x distribution
and compute the mean and standard deviation of the distribution.
x
has
—Select—

a binomial

an unknown

a normal

an approximately normal

a Poisson

a geometric
distribution with mean μx =
and standard deviation σx =  .

(b) Find the z value corresponding to x = 99.

z =

(c) Find P(x < 99).
(Round your answer to four decimal places.)
P(x < 99) =

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 99? Explain.
No, it would not be unusual because less than 5% of all such samples have means less than 99.
Yes, it would be unusual because more than 5% of all such samples have means less than 99.
Yes, it would be unusual because less than 5% of all such samples have means less than 99.
No, it would not be unusual because more than 5% of all such samples have means less than 99.

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