Question

Please show work for how to find the answer.

You are the producer for the television show Actuarial Idol. Each year, 1000 actuarial clubs audition forthe show The probability of a cdlub being accepted is 0.20. The number of members of an accepted club has a distribution with mean 20 and variance 20. Club acceptances and the numbers of club members are mutually independent. 7 Your annual budget for persons appearing on the show equals 10 times the expected number of persons plus 10 times the standard deviation of the number of persons. Calculate your annual budget for persons appearing on the show. (A) 42,600 (B) 44,200 (C) 45,800 (D) 47,400 (E) 49,000

Answer 1

Hello Sir/ Mam

Answer is Option E : 49,000

Given that:

Mean = 20, Variance = 20, hence, standard deviation = 4.472

Now, P(Selection) = 0.2

Total number of team =1000

Hence, the expected number of selected teams = 1000*0.2 = 200

Hence,

Budget = 10(200*20) + (4.472*200*10) = 48944.27 approximately equal to 49,000

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