IQ is normally distributed with a mean of 100 and a standard deviation of 15 a)

Question

IQ is normally distributed with a mean of 100 and a standard deviation of 15 a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 93. Write your answer in percent form. Round to the nearest tenth of a percent. P(IQ greater than 95)- b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. Write your answer in percent form. Round to the nearest tenth of a percent P(IQ less than 125)- c) In a sample of 500 people, how many people would have an IQ less than 110? people d) In a sample of 500 people, how many people would have an IQ greater than 140? people

Explanation / Answer

Solution:- mean = 100, sd = 15.

a) P(X > 95) = P(Z > (95-100)/15)

=  P(Z > -0.3333)

= 0.6293

= 62.93%

b) P(X < 125) = P(Z < (125-100)/15)

=   P(Z < 1.6667)

= 0.9525

= 95.25%

c) n = 500

P(X < 110) = P (Z < (110 - 100)/(15/sqrt(500))

= P( Z < 14.9071)

= 1

d) n = 500

P(X > 140) = P( Z > (140 - 100)/(15/sqrt(500))

= P(Z > 59.6284)

= 0

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