Question

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. use empirical rule to determine the following:
a) what percentage of people has an IQ score between 61 and 139?
b) what percentage of people has IQ score less than 87 or greater than 113?
c) what percentage of people has an IQ score greater than 113?

Answer 1

Using the Empirical Rule, the percentages are given as follows:

a) 99.7%.

b) 32%.

c) 16%.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

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

• Approximately 95% of the measures are within 2 standard deviations of  the mean.

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

Item a:

61 and 139 is within 3 standard deviations of the mean, hence the percentage is of 99.7%.

Item b:

87 and 113 is within one standard deviation of the mean, hence 68% of the data is within this interval and 100 - 68 = 32% of the data is outside this interval.

Item c:

Considering that the normal distribution is symmetric, and item b, this percentage is of 32%/2 = 16%.

More can be learned about the Empirical Rule at brainly.com/question/24537145

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