Suppose x has a distribution with a mean of 70 and astandard deviation of 15. Random samples of size
n = 36
are drawn.
(a) Describe the
x distribution
and compute the mean and standard deviation of thedistribution.
x
has  ---Select--- a binomial an unknown a geometric anapproximately normal a normal a Poisson distribution with
mean ?x =
and
standard deviation ?x=Â Â .
(b) Find the z value corresponding to
x = 75.
z =
(c) Find
P(x < 75).
(Round your answer to four decimal places.)
P(x < 75) =
(d) Would it be unusual for a random sample of size 36 from thex distribution to have a sample mean less than 75?Explain.
Yes, it would be unusual because less than 5% of all suchsamples have means less than 75.No, it would not be unusual becausemore than 5% of all such samples have means less than75.    No, it would not be unusual because lessthan 5% of all such samples have means less than 75.Yes, it wouldbe unusual because more than 5% of all such samples have means lessthan 75.
