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Lyrx [107]
3 years ago
6

"The manager for State Bank and Trust has recently examined the credit card account balances for the customers of her bank and f

ound that 20% have an outstanding balance at the credit card limit. Suppose the manager randomly selects 15 customers and finds 4 that have balances at the limit. Assume that the properties of the binomial distribution apply.a.What is the probability of finding 4 customers in a sample of 15 who have "maxed out" their credit cards?b.What is the probability that 4 or fewer customers in the sample will have balances at the limit of the credit card"
Mathematics
1 answer:
yuradex [85]3 years ago
4 0

Answer:

a

   P(X = 4 ) = 0.1876

b

   P(X \le 4)  =  0.8358

Step-by-step explanation:

From the question we are told that

The proportion that has outstanding balance is p = 0.20

The sample size is n = 15

Given that the properties of the binomial distribution apply, for a randomly selected number(X) of credit card

X \  \ ~ Bin (n , p )

Generally the probability of finding 4 customers in a sample of 15 who have "maxed out" their credit cards is mathematically represented as

P(X = 4 ) =  ^nC_4 * p^4 * (1 - p)^{n-4}

=> P(X = 4 ) =  ^{15}C_4 * (0.20)^4 * (1 - 0.20)^{15-4}

Here C stand for combination

=> P(X = 4 ) = 0.1876

Generally the probability that 4 or fewer customers in the sample will have balances at the limit of the credit card is mathematically represented as

P(X \le 4) =  [ ^{15}C_0 * (0.20)^0 * (1 - 0.20)^{15-0}]+[ ^{15}C_1 * (0.20)^1 * (1 - 0.20)^{15-1}]+\cdots+[ ^{15}C_4 * (0.20)^4 * (1 - 0.20)^{15-4}]

=>   P(X \le 4)  =  0.8358

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