Question

IQ scores (as measured by the Stanford-Binet intelligence test) are normally distributed with a mean of 100 and a standard deviation of 16. What percentage of the population has an IQ score between 110 and 124? (Round your answer to the nearest percentage point.)

Answer 1

ANSWER:

Given that,

IQ scores (as measured by the Stanford-Binet intelligence test) are normally distributed with a mean of 100 and a standard deviation of 16. What percentage of the population has an IQ score between 110 and 124? (Round your answer to the nearest percentage point.)

Mean = = 100

Stnadard deviation = = 16

We know that,

Z = (x-)/ = (x-100)/16

P(110 < X < 124) = P((110-100)/16 < (x-)/ < (124-100)/16)

P(110 < X < 124) = P(10/16 < Z < 24/16)

P(110 < X < 124) = P(0.63 < Z < 1.50)

P(110 < X < 124) = P(Z < 1.50)-P(Z < 0.63 )

P(110 < X < 124) = 0.93319-0.73565

P(110 < X < 124) = 0.19754

P(110 < X < 124) = 19.75 %

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