The following table shows the percentages of residents in a

The following table shows the percentages of residents in a large community when classified according to gender and presence of a particular allergy. For each part below, find to 3 decimal places the mean and standard deviation of the specified random variable. X stands for the number of persons having the allergy in a random sample of 20 persons. The mean is and the standard deviation is stands for the number of males having the allergy in a random sample of 20 males. The mean is and the standard deviation is Z stands for the number of females not having the allergy in a random sample of 20 females. The mean is and the standard deviation is

Solution

a)

Here,

p = allergy present = 25/100 = 0.25

Thus,

mean = n p = 20*0.25 = 5 [ANSWER]

standard deviation = sqrt(np(1-p)) = sqrt(20*0.25*(1-0.25)) = 1.936491673 [ANSWER]

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B)

Here,

p = allergy present given male= 16/(16+38) = 0.296296296

Thus,

mean = n p = 20*0.296296296 = 5.925925926 [ANSWER]

standard deviation = sqrt(np(1-p)) = sqrt(20*0.296296296*(1-0.296296296)) = 2.042081296 [ANSWER]

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C)

Here,

p = allergy present given female= 9/(9+37) = 0.195652174

Thus,

mean = n p = 20*0.195652174 = 3.91304348 [ANSWER]

standard deviation = sqrt(np(1-p)) = sqrt(20*0.195652174*(1-0.195652174)) = 1.774104849 [ANSWER]