Supposexhas a distribution with a mean of50and a standard deviation of27. Random samples of sizen=36are drawn.

(a)Describe thedistribution.

has a geometric distribution.

has an approximately normal distribution.

has a normal distribution.

has a Poisson distribution.

has an unknown distribution.

has a binomial 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=41. (Enter an exact number.)

z=

(c)FindP(<41). (Enter a number. Round your answer to four decimal places.)

P(<41) =

P(x bar < 41)

(d)Would it be unusual for a random sample of size36from thexdistribution to have a sample mean less than41? Explain.

No, it would not be unusual because more than 5% of all such samples have means less than 41.

No, it would not be unusual because less than 5% of all such samples have means less than 41.

Yes, it would be unusual because more than 5% of all such samples have means less than 41.

Yes, it would be unusual because less than 5% of all such samples have means less than 41.