Thank you 4.27 The mean height of adult men is approximately 69 inches; the mean

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4.27 The mean height of adult men is approximately 69 inches; the mean height of adult women is approximately 65 inches. The variance of height for both is 42 inches. Assume that husband-wife pairs occur without relation to height, and that heights are approximately normally distributed (a) What is the sampling distribution of the mean height of a couple? What are its parameters? (The variance of two statistically independent variables is the sum of the variances.) (b) What proportion of couples is expected to have a mean height that exceeds (c) In a collection of 200 couples, how many average heights would be expected to *(d) In what proportion of couples do you expect the wife to be taller than the hus 70 inches? exceed 70 inches? band?

Explanation / Answer

a)sampling distribution of mean height of couple will be normal

here mean height of couple =(69+65)/2 =67

and varaince =(42+42)/4 =8

also std deviaition =(8)1/2 =2.8284

b) proportion of heights below 70 =P(X<70) =P(Z<(70-67)/2.8284)= P(Z<1.0607) =0.8556

c)probability of height to exceed 70 inches p=1-0.8556 =0.1444

for expected number of couples having mean height greater then 70 inches =np =200*0.1444 =28.88 ~29

d)mean difference between male and female height =69-65=4

and std deviaiton =(42+42)1/2 =5.6569

for female height to be greater then men : P(X<0) =P(Z<(0-4)/5.6569) =P(Z<-0.7071)=0.2398

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