Question

Problem 2 Salaries for new assistant professors at State College are normally distributed with a mean of $80000 and a standard deviation of $7000 We randomly survey 20 teachers from that district, let X be the salary of a randomly selected teacher at State, and let X be the average salary of 20 randomly selected teachers bxpan a.(3%)X~ b, (3%)8~ (3%) Normal Norma, D Find the probability that an individual teacher earns more than $65,000. P(X> 65000) d. (3%) Find the probability that the average salary for the sample is more than $65,000. P> 65000) e. (396) Frd te 90th percertie forthe average teachers' salary for samples of 20 teachers. PR <a) 0.9 thena-

Answer 1

(a)

b:

Since it is given that X has normal distribution so Xbar will also have normal distribution with following parameters

$mu_{ar{x}}=mu=80000$

and'

Hence,

c)

The z-score for X = 65000 is

So the required probability is

d)

The z-score for is

$z=rac{65000-80000}{1565.2476}=-9.58$

So the required probability is

​

e)

Here we need z-score that has 0.90 area to its left. The z-score 1.28 has 0.90 area to its left. The required a is