Question

32% of college students say they use credit cards because of the rewards program you randomly selected 10 college students and ask each to name the reason he or she uses credit cards find the probability that the number of college students who say they use credit cards because of the rewards program is a exactly to be more than two and see between 2 and 5 exclusive

Answer 1

a. 0.6687

b. 0.4821

Explanation:

Attached is an image showing the step by step workings.

Answer 2

P(X > 2) = 0.6687

P(2 < X < 5) = 0.4821

Explanation:

This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = sample size = 10

x = Number of successes required = more than 2, then between 2 and 5.

p = probability of success = probability that a college student will say they use credit cards because of the rewards program = 0.32

q = probability of failure = 1 - 0.32 = 0.68

For more than 2

a) P(X > 2) = 1 - P(X ≤ 2) = 1 - [P(X=0) + P(X=1) + P(X=2)] = 1 - [0.0211392282 + 0.09947872095 + 0.21066082083] = 0.66872123002 = 0.6687

For between 2 and 5 exclusive

P(2 < X < 5) = P(X=3) + P(X=4) = 0.26435867712 + 0.21770714587 = 0.482065823 = 0.4821

Hope this Helps!!!