1- The scale of scores on the WAIS is approximately Normal with mean 100 and sta

Question

1- The scale of scores on the WAIS is approximately Normal with mean 100 and standard deviation 15. Answer the following questions:

(a) The organization MENSA, which calls itself “the high-IQ society”, requires an IQ score of 130 or higher for membership. What percent of adults would qualify for membership?

(b) Corrine scores 118 on such a test. How far away from the mean is she (or how many standard deviation units away from the mean is she)?

(c) Corrine scores higher than what percent of all adults?

(d) Individuals with WAIS scores below 70 are considered mentally retarded, when, for example, applying for Social Security disability benefits. By this criterion, what percentage of adults is retarded?

2- Suppose that the weight of navel oranges is normally distributed with mean µ = 8 ounces, and standard deviation = 1.5 ounces. We can write X ~ N(8, 1.5).

Find the interquartile range of this distribution of X

Explanation / Answer

Question-1

Part-a

Let X denote the IQ then X~N(100,15)

Percent of adults that would qualify for member ship

=100*P(X>=130)

=100*(1-P(X<130))

=100*(1-0.9772) using excel function =NORMDIST(130,100,15,TRUE)

=100* 0.0228

=2.28%

Part-b

Z-score=(118-Mean)/SD =(118-100)/15 = 1.2

Hence Corrine is 1.2 standard deviation away from mean.

Part-c

Corrine’s scores higher than the percent of all adults = 100*P(Z<1.2)

=100*0.8849 using excel function =normsdist(1.2)

=88.49%

Part-d

The percent of adults who are retarded is=100*P(X<70)

=100*0.0228 using excel function =NORMDIST(70,100,15,TRUE)

=2.28%

Question-2

First quartiles Q1 is such that P(X<Q1)=0.25

Using excel function =NORMINV(0.25,8,1.5) we get Q1=6.99

Third quartiles Q3 is such that P(X<Q3)=0.75

Using excel function =NORMINV(0.75,8,1.5) we get Q3=9.01

So, interquartile range=Q3-Q1=9.01-6.99 =2.02

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