Question

IQ scores for Wayne High School teachers are normally distributed according to N(120,20). In what range does middle 68% of people in the group score on the test?

Answer 1

The middle 68% of Wayne High School teachers' IQ scores, which are normally distributed with a mean of 120 and a standard deviation of 20, range between 100 and 140.

Step-by-step explanation:

The question is asking for the range within which the middle 68% of the IQ scores for Wayne High School teachers fall, given that IQ scores are normally distributed with a mean (average) of 120 and a standard deviation of 20. According to the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data, about 68% of the data lies within one standard deviation of the mean. Therefore, the middle 68% of IQ scores will range from one standard deviation below the mean to one standard deviation above the mean.

To calculate this, subtract one standard deviation from the mean and add one standard deviation to the mean:

• Lower bound = Mean - Standard deviation = 120 - 20 = 100
• Upper bound = Mean + Standard deviation = 120 + 20 = 140

So, the middle 68% of IQ scores for teachers at Wayne High School will be between 100 and 140.