Question

Given a normal distribution with μ=100 and σ=10, complete parts​ (a) through​ (d). Show ALL Work.

a. What is the probability that X>80​?

​(Round to four decimal places as​ needed.)

b. What is the probability that X<95​?

(Round to four decimal places as​ needed.)

c. What is the probability that X<90 or X>130​?

(Round to four decimal places as​ needed.)

d. 99​% of the values are between what two​ X-values (symmetrically distributed around the​ mean)?

99​%of the values are greater than ____ and less than ____

​(Round to two decimal places as​ needed.)

Answer 1

a)

b)

C)

d)

We want to find '-a' and 'a' such that

Since Normal distribution is symmetric about the mean, so

So, 99​%of the values are greater than -2.58 and less than 2.58