1. Supposexhas a distribution with a mean of80and a standard deviation of3. Random samples of sizen=36are drawn.

(a) Describe thexbar distribution. i. xbar has a binomial distribution.

ii. xbar has an unknown distribution.

iii. xbar has a Poisson distribution.

iv. xbar has an approximately normal distribution.

v. xbar has a geometric distribution.

vi. xbar 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=81. (Enter an exact number.) z= (c) FindP(<81). (Enter a number. Round your answer to four decimal places.) P(<81) =P(x bar < 81)

2. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

= 8; = 2

P(7 x 11) =

3. What percentage of the area under the normal curve lies as given below?

(a)to the right of (Enter an exact number.) % (b)between 2 and + 2 (Enter an exact number). % (c)to the right of + 3 (Enter a number. Use 2 decimal places.) %