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Chapter 5: Q. 5.8 (page 217)

A randomly chosen IQtest taker obtains a score that is approximately a normal random variable with mean 100and standard deviation 15. What is the probability that the score of such a person is

(a) more than 125;

(b) between 90and 110?

Short Answer

Expert verified

(a) Probability that the score of a person more than 125is 0.0478

(b) Probability that the score of a person between90and110is0.4972

Step by step solution

01

Step:1 Find the Probability that the score of a person more than 125 (part a)

Define Xas a random variable that represents a random person's IQ. We're told that data-custom-editor="chemistry" X~N100,152. That is, Y=X-10015has a conventional normal distribution with a cumulative distributionϕ.

P(X>125)=1-P(X≤125)=1-PX-10015≤125-10015

=1-Φ53≈0.0478

02

Step:2 Find the Probability that the score of a person between 90 and 110 (part b)

P(X∈(90,110))=P(X≤110)-P(X≤90)

=PX-10015≤110-10015-PX-10015≤90-10015

=Φ23-Φ-23=2Φ23-1=0.4972

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