Question

Scores on exam 2 for statistics are normally distributed with mean 70 and standard deviation 15.

a. Find a, if P(x>a)= 0.9595

b.What is the probability that a randomly selected score is above 65?

Answer 1

Part a

We are given

P(x>a)= 0.9595

P(x<a)= 1 - 0.9595 = 0.0405

We are given mean = 70, SD = 15

Z for probability 0.0405 is given as -1.74491.

Z = (a – mean) / SD

-1.74491 = (a – 70) / 15

a = 70 - 15*1.74491

a = 43.82635

Part b

Here, we have to find P(X>65)

P(X>65) = 1 – P(X<65)

Z = (X – mean) / SD

Z = (65 - 70)/15

Z = -0.33333

P(Z<-0.33333) = P(X<65) = 0.369441

(by using z-table)

P(X>65) = 1 – P(X<65)

P(X>65) = 1 – 0.369441

P(X>65) = 0.630559

Required probability = 0.630559