Question 5

Test scores on a university admissions test are normally distributed, with a mean of 500 and a standard deviation of 100.

4 marks a. What is the probability that a randomly selected applicant scores between 425 and 575?

P(425 x 575) =

This means P(z) between 425 to 575

Given that Z =

(z = 425) = = -0.75

z = 575 = = 0.75

P(425 x 575) = P(-0.75 z 0.75) =

P(z = 0.75) = 0.77337

P(z = -0.75) .22663

P(425 x 575) = P(-0.75 z 0.75) = [P(z = 0.75) P(z = -0.75)] = 0.77337 - 0.22663= 0.54674

4 marks b. What is the probability that a randomly selected applicant scores 625 or more?

Given that z =

P(x 625) = P(z )=

= P(z 1.25) = 1.25 - 0.89435= 0.35565

The probability the a randomly selected applicant scores between 625 or more on their test scores is roughly 36%.

2 marks c. What is the probability that a randomly selected applicant scores less than 500?

P(x < 500) = P(z < )

= P(z < 0) = 0.50000

The probability the a randomly selected applicant scores less than 500 on their test scores is 50%.

4 marks d. Twenty per cent of test scores exceed what value?