Question

LSAT test scores are normally distributed with a mean of 153 and a standard deviation of 10. Find the probability that a randomly chosen test-taker will score between 133 and 173. (Round your answer to four decimal places.)

Answer 1

Solution:

We are given

Mean = 153

SD = 10

We have to find P(133<X<173)

P(133<X<173) = P(X<173) – P(X<133)

Find P(X<173)

Z = (X – mean)/SD

Z = (173 - 153)/10

Z = 2

P(Z<2) = P(X<173) = 0.97725

(by using z-table)

Now find P(X<133)

Z = (133 - 153)/10

Z = -2

P(Z<-2) = P(X<133) = 0.02275

(by using z-table)

P(133<X<173) = P(X<173) – P(X<133)

P(133<X<173) = 0.97725 - 0.02275

P(133<X<173) = 0.9545

Required probability = 0.9545