Question

g Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 12. Use the empirical rule to determine the following. ​(a) What percentage of people has an IQ score between 76 and 124​? ​(b) What percentage of people has an IQ score less than 64 or greater than 136​? ​(c) What percentage of people has an IQ score greater than 136​?

Answer 1

Answer:

a) 95% of people has an IQ score between 76 and 124​.

b) 0.3% of people has an IQ score less than 64 or greater than 136​.

c) 0.15% of people has an IQ score greater than 136

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 100

Standard deviation = 12

​(a) What percentage of people has an IQ score between 76 and 124​? ​

76 = 100 - 2*12

124 = 100 + 2*12

So within 2 standard deviations of the mean, and the percentage is 95%.

(b) What percentage of people has an IQ score less than 64 or greater than 136​?

64 = 100 - 3*12

136 = 100 + 3*12

99.7% of people has scores between 64 and 136. So 100 - 99.7 = 0.3% of people has an IQ score less than 64 or greater than 136​.

​(c) What percentage of people has an IQ score greater than 136​?

0.3% of people has an IQ score less than 64 or greater than 136​.

Since the normal distribution is symmetric, 0.3%/2 = 0.15% are below 64 are 0.15% are above 136.