Question

IQ test scores are standardized to produce a normal distribution with a mean of = 100 and a standard deviation of = 15. Find the proportion of the population for the following IQ score. For your answer, convert each proportion into a percentage whose value is computed to 2 decimal places. Sketch a distribution to help you visualize the problem. IQ score greater than 135

Answer 1

0.01

Explanation:

Using the z score formula

z = (x-μ)/σ,

where x is the raw score = 135

μ is the population mean = 100

σ is the population standard deviation = 15

z = 135 - 100/15

z = 2.33333

P-value from Z-Table:

P(x<135) = 0.99018

P(x>135) = 1 - P(x<135)

P(x > 135) = 1 - 0.99018

= 0.0098153

Approximately to 2 decimal places

= 0.01

Therefore, the proportion of the population for the following IQ score of 135 is 0.01