5.Assume that a population of thousands of people whose responses were used to d

Question

5.Assume that a population of thousands of people whose responses were used to develop the anxiety test had scores that were normally distributed with = 30 and = 10. What proportion of people in this population would have anxiety scores within each of the following ranges of scores?

a.Below 20

b.Above 30

c.Between 10 and 50

d.Below 10

e.Below 50

f.Above 50

g.Either below 10 or above 50 Assuming that a score in the top 5% of the distribution would be considered extremely anxious, would a person whose anxiety score was 50 be considered extremely anxious?

(Warner) Warner, Rebecca M. Applied Statistics: From Bivariate Through Multivariate Techniques, 2nd Edition. SAGE Publications, Inc, 20120410. VitalBook file.

Explanation / Answer

Ans:

Given that

mean=30 and standard deviation=10

a)

z(20)=(20-30)/10=-1

P(z<-1)=0.1587

b)

z(30)=(30-30)/10=0

P(z>0)=0.5

c)

z(10)=(10-30)/10=-2

z(50)=(50-30)/10=2

P(-2<z<2)=P(z<2)-P(z<-2)=0.9773-0.0228=0.9545

d)

z(10)=(10-30)/10=-2

P(z<-2)=0.0228

e)

z(50)=(50-30)/10=2

P(z<2)=0.9773

f)z(50)=2

P(z>2)=0.0228

g)

P(z<-2 or z>2)=P(z<-2)+P(z>2)=0.0228+0.0228=0.0456

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