Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 13.

Use the empirical rule to determine the following.

​(a) What percentage of people has an IQ score between 87 and 113​?

​(b) What percentage of people has an IQ score less than 87 or greater than 113​?

​(c) What percentage of people has an IQ score greater than 139?

Answer 1

This is a normal distribution question with


a) P(87.0 < x < 113.0)=?


This implies that


b) P(x < 87.0)=?
The z-score at x = 87.0 is,

This implies that

P(x > 113.0)=?
The z-score at x = 113.0 is,

This implies that

so,
P(x < 87) or P(x > 113) = 0.1587 + 0.1587 = 0.3174

c) P(x > 139.0)=?
The z-score at x = 139.0 is,

This implies that

PS: you have to refer z score table to find the final probabilities.
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