Question

Recent test scores on the Law School Admission Test (LSAT) are normally distributed with a mean of 162.4 and a standard deviation of 15.9. What is the probability that the mean of 8 randomly selected scores is less than 161?

Answer 1

0.40166

Explanation:

When given random number of samples, we solve using the z score formula:

z = (x-μ)/σ/√n where

x is the raw score= 161

μ is the population mean = 162.4

σ is the population standard deviation = 15.9

n is random number of samples = 8

Hence,

z = 161 - 162.4/15.9/√8

z = -0.24904

Probability value from Z-Table:

P(x<161) = 0.40166

The probability that the mean of 8 randomly selected scores is less than 161 is 0.40166