Supposexhas a distribution with a mean of40and a standard deviation of21. Random samples of sizen=36are drawn.

(a)Describe the X distribution.

has an unknown distribution.

has a binomial distribution.

has a geometric distribution.

has a Poisson distribution.

has an approximately normal distribution.

has a normal distribution.

Compute the mean and standard deviation of the distribution. (For each answer, enter a number.)

=

mu sub x bar =

=

sigma sub x bar =

(b)Find thezvalue corresponding to X=47. (Enter an exact number.)

z=

(c)FindP(<47). (Enter a number. Round your answer to four decimal places.)

P(<47) =

P(x bar < 47)

(d)Would it be unusual for a random sample of size36from thexdistribution to have a sample mean less than47? Explain.

Yes, it would be unusual because less than 5% of all such samples have means less than 47.

No, it would not be unusual because less than 5% of all such samples have means less than 47.

Yes, it would be unusual because more than 5% of all such samples have means less than 47.

No, it would not be unusual because more than 5% of all such samples have means less than 47.