Steve, Katerina and Jess are three students who have agreed to take part in a psychology experiment. Each

student is to answer several sets of multiple-choice questions. Each set has the same number of questions,

n, where n is a number greater than 20. For each question there are four possible options (A, B, C or D), of

which only one is correct.

From these sets of 25 questions being completed by many students, it has been found that the time, in minutes, that any student takes to answer each set of 25 questions is another random variable, W, which is normally distributed with mean a and standard deviation b.

It turns out that, for Jess, Pr(Y = 18) = Pr(W = 20) and also Pr(Y = 22) = Pr(W = 25).

Calculate the values of a and b, correct to three decimal places.

I dont get this question

Pr(Y>=22) = .381566

So you know that W is a normally distributed variable and

Pr(W >= 20) = .955268

Pr(W >= 25) = .381566

Flip them to get the CDF

CDF of W at 20 = 1-.955268 = 0.044732

CDF of W at 25 = 1-.381566 = 0.618434

Looking them up it a Z table gives

Z at 20 is -1.7

Z at 25 is 0.3

Remember that the formula for Z is Z=(W-mean)/stddev

So -1.7 = (20-a)/b and .3 = (25-a)/b

Solve that for a and b and you get

a = 24.25, b = 2.500

Note that you had a=24.246 which is the same thing only a bit more precise. My Z values were probably rounded too much.