#271 The intelligence quotient (IQ) is a measure

The intelligence quotient (IQ) is a measure - Math

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Free Chegg Question

The intelligence quotient (IQ) is a measure of mental ability. Qs are normally distributed with a mean of 100 and a standard deviation of 15 A. What is the probability of randomly selecting an individual with an IQ greater than 120? Give the answer as a percent rounded to one decimal place.

B. Individuals within the "borderline deficient" classification have IQs below 70. What percent of individual fall in this classification? Give the answer as a percent rounded to one decimal place.

C. Individuals with an IQ in the "normal" classification have IQs in the range of 85-115 What percent of individual fall in this classification? Give the answer as a percent rounded to one decimal place.

D. Find a symmetric interval about the mean IQ such that 50% of all IQs lie in this IQ score interval. What are the endpoints of this interval called (give the vocabulary words)? Give these values rounded to whole numbers.

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Free Chegg Answer

a. P(IQ>120) = P(Ziq > 120-100/15) = P(Ziq > 1.33) = 1-.9082 = .0918

b. P(IQ<70) = P(Ziq < 70-100/15) = P(Ziq<-2) = .0228

c. P(85<IQ<115) = P(85-100/15 <Ziq<115-100/15) = P(-1<Z<1) = .6813

d. 50% of all IQs will lie between ?

So, P(-z1<Z<z1) = .50

Z is .675 from the Z tables such that P(0<Z<.675) = .25, and since the Z tables are symmetrical we have z1 = .675

So, end points are -.675*15+100 to .675*15+100 = 89.875 to 110.125

So, intervel for 50% of all IQs aroud mean is {89.875 , 110.125}