iq scores are normally distributed with a mean of 100 and a standard deviation of 15. using the empirical…

iq scores are normally distributed with a mean of 100 and a standard deviation of 15. using the empirical rule, determine the interval that would represent the middle 68% of iq scores.

iq scores are normally distributed with a mean of 100 and a standard deviation of 15. using the empirical rule, determine the interval that would represent the middle 68% of iq scores.

Answer

Explanation:

Step1: Recall the empirical rule

The empirical rule (68 - 95 - 99.7 rule) for a normal distribution states that approximately 68% of the data lies within 1 standard deviation of the mean.

Step2: Calculate the lower and upper bounds

Given the mean (\mu = 100) and standard deviation (\sigma=15). The lower bound is (\mu - \sigma). [100 - 15=85] The upper bound is (\mu+\sigma). [100 + 15 = 115]

Answer:

The interval that represents the middle 68% of IQ scores is ((85,115))