27% of college students, say they use credit cards because of the rewards progra

Question

27% of college students, say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses cards. find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two. (b) more than two and (c) between two and five inclusive. If covariant, use technology is find the probabilities. (a) P(2) = (b) P(x > 2) = (c) P(2 lessthanorequalto x lessthanorequalto 5) =

Explanation / Answer

Solution:-

p = 27/100

p = 0.27

a) The probability that number of college students who use there credit cards becuase of rewards program is exactly two is 0.2646.

n = 10, x = 2

By applying binomial distribution:-

P(x, n, p) = nCx*p x *(1 - p)(n - x)

P(x = 2) = 0.2646

b) The probability that number of college students who use there credit cards becuase of rewards program is more than two is 0.534.

n = 10, x = 2

By applying binomial distribution:-

P(x, n, p) = nCx*p x *(1 - p)(n - x)

P(x > 2) = 0.534

c) The probability that number of college students who use there credit cards becuase of rewards program is between two and five inclusive is 0.7694.

n = 10, x = 2

By applying binomial distribution:-

P(x, n, p) = nCx*p x *(1 - p)(n - x)

P(2 < x < 5) = P( x > 2) - P(x > 5)

P(2 < x < 5) = 0.7981 - 0.0287

P(2 < x < 5) = 0.7694

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