Question

question
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 95% of iq scores.
answer attempt 1 out of 2

Explanation:

Step1: Recall the empirical rule for normal distribution

For a normal distribution, the empirical rule states that approximately 95% of the data lies within \( \mu \pm 2\sigma \), where \( \mu \) is the mean and \( \sigma \) is the standard deviation.
Given \( \mu = 100 \) and \( \sigma = 15 \).

Step2: Calculate the lower bound

The lower bound of the interval is \( \mu - 2\sigma \).
Substitute the values: \( 100 - 2\times15 = 100 - 30 = 70 \).

Step3: Calculate the upper bound

The upper bound of the interval is \( \mu + 2\sigma \).
Substitute the values: \( 100 + 2\times15 = 100 + 30 = 130 \).

Answer:

The interval representing the middle 95% of IQ scores is \( (70, 130) \)