IQ tests are standardized to a normal model with a mean of 100 and standard devi

Question

IQ tests are standardized to a normal model with a mean of 100 and standard deviation of 16 That is IQ is N (100, 16) In what interval would you expect the central 95% of IQ scores to be found? About what percent of people should have IQ scores above 116 About what % of people should have IQ scores between 80 and 84? About what percent of people should have IQ scores above 132? What cutoff value bounds The highest 5% of all IQs? The lowest 25% of the IQs The middle 80% of the IQs What IQ represents 15^th percentile What IQ represents 98^th percentile

Explanation / Answer

a) According to Emperical rule, 95% scores fall from 2 standard deviation from the mean.

The limit is therefore, mu-2sd to mu+2sd=100-2*16 to 100+2*16=68 to 132.

b) From information, Xi=116, Xbar=100, s=16. Substitute the values in following equation and obtain z score.

Z=(Xi-Xbar)/s=(116-100)/16=1

P(X>116)=P(Z>1)=0.1587~15.87%

c) Find Z score scorrespondng to Xi=80 and 84

Z1=(80-100)/16=-1.25 and Z2=(84-100)/16=-1

P(80<X<84)=P(-1.25<Z<-1)=0.3944-0.3413=0.0531~5.31%

d) Z=(132-100)/16=2

P(X>132)=P(Z>2)=0.0228~2.28%

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