Question

The Law School Admission Test (LSAT) is a standardized exam issued four times a year for prospective law school candidates. The test is designed to assess a candidate in reading comprehension, as well as in their logical and verbal reasoning. The scores are adjusted to form a normal distribution with most scores falling in the 120 and 180 range, with a mean of 149 and a standard deviation of 8.5.

If a candidate who wrote the exam were selected at random, what is the probability that...

Q1-1: They achieved a score that was less than 170 on the LSAT?
Q1-2: They achieved a score that was more than 125 on the LSAT?
Q1-3: They achieved an LSAT score that was between 160 and 173 on the LSAT?

Answer 1

Given,

= 149 , = 8.5

We convert this to standard normal as

P( X < x) = P (Z < x - / )

a)

P(X < 170) = P( Z < 170 - 149 /8.5)

= P( Z < 2.4706)

= 0.9933

b)

P( X > 125) = P( Z > 125 - 149 / 8.5)

= P( Z > -2.8235)

= P( Z < 2.8235)

= 0.9976

c)

P( 160 < X < 173) = P( X < 173) - P( X < 160)

= P( Z < 173 - 149 / 8.5) - P( Z < 160 - 149 / 8.5)

= P( Z < 2.8235) - P( Z < 1.2941)

= 0.9976 - 0.9022

= 0.0954