Supposexhas a distribution with a mean of70and a standard deviation of36. Random samples of sizen=64

are drawn.

(a) Describe thexdistribution

and compute the mean and standard deviation of the distribution.

x

has

---Select---

a geometric

an unknown

a Poisson

a binomial

a normal

an approximately normal

distribution withmean_x=

andstandard deviation_x=.

(b) Find thezvalue corresponding tox=74.5.

z=

(c) FindP(x<74.5).

(Round your answer to four decimal places.)

P(x<74.5) =

(d) Would it be unusual for a random sample of size64from thexdistribution to have a sample mean less than74.5? Explain.

No, it would not be unusual because less than 5% of all such samples have means less than 74.5.

No, it would not be unusual because more than 5% of all such samples have means less than 74.5.

Yes, it would be unusual because less than 5% of all such samples have means less than 74.5.

Yes, it would be unusual because more than 5% of all such samples have means less than 74.5.