Supposexhas a distribution with a mean of80and a standard deviation of51. Random samples of size

n=36

are drawn.

(a) Describe the xdistribution and compute the mean and standard deviation of the distribution. x= has ---Select--- a normal a binomial an unknown an approximately normal a geometric a Poisson distribution with mean_x= ____-and standard deviation_x= .

(b) Find thezvalue corresponding to x=71.5.

z=

(c) Find

P(x<71.5).

(Round your answer to four decimal places.) P(x<71.5) =

(d) Would it be unusual for a random sample of size36from thexdistribution to have a sample mean less than71.5? Explain. =Yes, it would be unusual because less than 5% of all such samples have means less than 71.5.

=No, it would not be unusual because more than 5% of all such samples have means less than 71.5.

=Yes, it would be unusual because more than 5% of all such samples have means less than 71.5.

=No, it would not be unusual because less than 5% of all such samples have means less than 71.5.