Question

Assume that adults have IQ scores that are normally distributed with a mean of [mean] and a standard deviation [standard deviation]. Find the probability that a randomly selected adult has an IQ less than [IQ value].

Answer 1

To find the probability that a randomly selected adult has an IQ less than a specific value, calculate the z-score and use the standard normal distribution table or a calculator. Subtract the probability associated with the lower z-score from the probability associated with the higher z-score to find the probability between the two values.

Step-by-step explanation:

To find the probability that a randomly selected adult has an IQ less than a specific value, you need to standardize the value using the standard normal distribution. First, calculate the z-score using the formula (IQ value - mean) / standard deviation. Then, use the standard normal distribution table or a calculator to find the corresponding probability. The probability is the area under the curve to the left of the z-score.

In this case, you would calculate the z-scores for IQ values of 85 and 125. Let's assume the mean IQ is 105 and the standard deviation is 20.

For 85, the z-score is (85 - 105) / 20 = -1.

For 125, the z-score is (125 - 105) / 20 = 1.

Using the standard normal distribution table or a calculator, you can find the probabilities associated with these z-scores. Subtract the probability associated with the z-score of 85 from the probability associated with the z-score of 125 to find the probability that a randomly selected adult has an IQ between 85 and 125.