In Exercises 13-20, assume that adults have IQ scores that are normally distribu
ID: 3135312 • Letter: I
Question
In Exercises 13-20, assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wecbsler test). For a randomly selected adult, find the indicated probability or IQ score. Round IQ scores to the nearest whole number. 13. Find the probability of an IQ less than 85. 14. Find the probability of an IQ greater than 70 (the requirement for being a statistics textbook author). 15. Find the probability that a randomly selected adult has an IQ between 90 and 110 (referred to as the normal range.) 16. Find the probability that a randomly selected adult has an IQ between 110 and 120 (referred to as bright normal). 17. Find P_90, which is the IQ score separating the bottom 90% from the top 10%. 18. Find the first quartile Q_1, which is the IQ score separating the bottom 25% from the top 75%. 19. Find the third quartile Q_3, which is the IQ score separating the top 25% from the others.Explanation / Answer
13.
Z value for 85, z=(85-100)/15 =-1
P( x <85) = P( z < -1) = 0.1587
14.
Z value for 70, z=(70-100)/15 =-2
P( x >70) = P( z >-2) = 0.9772
15.
Z value for 90, z=(90-100)/15 =-0.67
Z value for 110, z=(110-100)/15 =0.67
P( 90<x<110) = P( -0.67<z<0.67)
= 0.7486 - 0.2514 =0.4972
16.
Z value for 120, z=(120-100)/15 =1.33
Z value for 110, z=(110-100)/15 =0.67
P( 110<x<120) = P( 0.67<z<1.33)
= 0.9082-0.7486 =0.1596
17.
Z value for top 10% =1.282
X=100+1.282*15=119.23
=119( rounded)
18.
Z value for top 75% =-0.674
X=100-0.674*15=89.89
=90( rounded)
19.
Z value for top 25% =0.674
X=100+0.674*15=110.11
=110( rounded)