The following table shows the percentages of residents in a large cormmunity whe

Question

The following table shows the percentages of residents in a large cormmunity when classified eccording to gender and presence of a particular allergy. For eech part below, find to 3 decimal places the mean and standard deviation of the specified random variable. Allergy Present Absent (a) X stands for the number of persons having the allergy in a randan sample of 140 persons The mean is a nd the standard deviation is (b) Y stands far the number of males having the allergy in a random sample of 140 males The mean is and the standard deviaton is ing the allergy in a ra (c) Z stands for the number of fermales nat ha The mean is ndom sample af 140 fernales. and the standard deviatianbs

Explanation / Answer

Solution:

(a) Here given,
p = allergy present = 25/100 = 0.25

Thus,
mean = n p = 140*0.25 = 35

standard deviation = sqrt(np(1-p)) = sqrt(140*0.25*(1-0.25)) = 5.1235

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(b) Here given,

p = allergy present given male= 15/(15+37) = 0.2885
Thus,
mean = n p = 140* 0.2885 = 40.39

standard deviation = sqrt(np(1-p)) = sqrt(140*0.2885*(1- 0.2885)) = 5.3607

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(c) Here given,
p = allergy present given female = 10/(10+38) = 0.2083
Thus, mean = n p = 140*0.2083 = 29.1620
standard deviation = sqrt(np(1-p)) = sqrt(140*0.2083*(1-0.2083)) = 4.8049

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