Question

The Stanford-Binet IQ Test is a normal curve with a mean of 100 and a standard deviation of 20. Estimate the probability that a randomly selected person has an IQ between 90 and 110?

A. 71.4%
B. 21.3%
C. 38.3%
D. 54.6%

Answer 1

To estimate the probability that a randomly selected person has an IQ between 90 and 110, we use the normal distribution table or calculator. Standardize the IQ values using the z-score formula, then find the area between the z-scores to determine the probability.

Step-by-step explanation:

To estimate the probability that a randomly selected person has an IQ between 90 and 110, we need to find the area under the normal curve between these two IQ values. The mean of the IQ test is 100 and the standard deviation is 20.

First, we need to standardize the IQ values using the formula: z = (x - mean) / standard deviation. For x = 90, z = (90 - 100) / 20 = -0.5. For x = 110, z = (110 - 100) / 20 = 0.5.

Next, we use a standard normal distribution table or calculator to find the area between these two z-scores. The area between -0.5 and 0.5 is approximately 0.3829. This represents the probability that a randomly selected person has an IQ between 90 and 110.