Question

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 15. Find the probability that a randomly selected adult has an IQ less than 115.

Answer 1

SOLUTION:

From given data,

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 15. Find the probability that a randomly selected adult has an IQ less than 115.

Mean = = 100

Standard deviation = =15

We know that,

Z = ( X - ) / = ( X - 100 ) / 15

The probability that a randomly selected adult has an IQ less than 115.

P(X < 115) = P(( X - ) / < ( 115 - 100 ) / 15)

P(X < 115) = P(Z < 15/ 15)

P(X < 115) = P(Z < 1)

P(X < 115) = 0.84134 (from z score table as shown below)

There fore the probability = 0.84134