Chapter 7: Q.96 (page 438)

A typical adult has an average IQ score of $105$ with a standard deviation of $20$ . If $20$ randomly selected adults are given an IQ test, what are the probability that the sample mean scores will be between $85$ and $125$ points?

Short Answer

Expert verified

The probability that the sample mean scores will be between $85$ and $125$ points is $1$ .

Step by step solution

Given Information

what is the probability that the sample mean scores will be between $85$ and $125$ points?

Explanation

$Letvariable X represent I Q score of a person. The distribution of X :$

$X ~ N (105, 20)$

The distribution of the average score of 20 people

$\bar{X} ~ N (105, \frac{20}{\sqrt{20}}) ~ N (20, \sqrt{20})$

Finding the wanted probability:

localid="1650524594045" $P (85 < X < 125) = P (\frac{85 - 105}{\sqrt{20}} < \frac{\bar{X} - 105}{\sqrt{20}} < \frac{125 - 105}{\sqrt{20}})$

$= ϕ (\frac{125 - 105}{\sqrt{20}}) - ϕ (\frac{85 - 105}{\sqrt{20}})$

$= ϕ (4.47) - ϕ (- 4.47)$

$= 2 ϕ (4.47) - 1$

= $2 - 1$

$= 1$

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A typical adult has an average IQ score of $105$ with a standard deviation of $20$ . If $20$ randomly selected adults are given an IQ test, what are the probability that the sample mean scores will be between $85$ and $125$ points?

Short Answer

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Explanation

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A typical adult has an average IQ score of 105with a standard deviation of 20. If 20randomly selected adults are given an IQ test, what are the probability that the sample mean scores will be between 85 and 125 points?

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Theoretical and Mathematical Physics

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Probability and Statistics

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Study anywhere. Anytime. Across all devices.

A typical adult has an average IQ score of $105$ with a standard deviation of $20$ . If $20$ randomly selected adults are given an IQ test, what are the probability that the sample mean scores will be between $85$ and $125$ points?