IQ Scores. In Exercises 6 – 9, assume that adults have IQ scores that are normal

Question

IQ Scores. In Exercises 6 – 9, assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. For a randomly selected adult, find the indicated probability or IQ score. Round IQ scores to the nearest whole number.

6. Find the probability of an IQ less than 75.

7. Find the probability that a randomly selected adult has an IQ between 70 and 115.

8. Find P65, which is the IQ separating the bottom 65% from the top 35%.

9. Find the third quartile Q3, which is the IQ score separating the top 25% from the others.

Explanation / Answer

Mean is 100 and s is 15

z is given as (x-mean)/s

a) P(x<75)=P(z<(75-100)/15)=P(z<-1.67) or 1-P(z<1.67), from normal distribution table we get 1-0.9525=0.0475

b) P(70<x<115)=P((70-100)/15<z<(115-100)/15)=P(-2<z<1) or P(z<1)-(1-P(z<2))=0.8413-(1-0.9772)=0.8185

c) for 65%, the z value is given from the normal distribution table as 0.39, thus answer is mean+s*z=100+15*0.39= 105.85

d) for Q3 i.e 75%, the z value from normal table is 0.68, thus answer is mean+s*z=100+15*0.68=110.2

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