Question

21. A gym has 2500 members. The ages of members have a normal distribution with mean of 47 years and standard deviation of 12 years. How many members have ages between [23,71]? 22. The ages of members of a gym have a normal distribution with mean of 47 years and standard deviation of 12 years. The z - score of age of a gym member is 2.2. How old is this member? 23. About 45% of the population in a town has blood that is Group 0. If we select 20 persons randomly, find the probability that at most 6 of them have blood that is Group 0.

Answer 1

Solution to 21)

Given μ = 47 and σ = 12

So,

μ - 2σ = 47 - 2(12) = 23

μ +2σ = 47 + 2(12) = 71

And two-sigma includes 95 percent, so the number of members aging between [23,71] is

= 2500*0.95 = 2375

Solution to 22)

X = μ + σZ = 47 + 12(2.2) = 73.4 years

Solution to 23)

Let p be the probability that person has blood Group O

n = 20 is sample size

Let the random variable X denotes the number of persons having blood Group O

So X ~ Binomial (20, 0.45)

So, P(X = x) = (nCx)p^{​​​​​​x}(1-p)^n-x

To find probability that atmost 6 person have blood Group O, so we need to find P(X ≤ 6)

P(X ≤ 6) = 0.1299337886