Question

​37% 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 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​ two, (b) more than​ two,

Answer 1

Explanation:

We would assume a binomial distribution for the number of college students that said they use credit cards because of the rewards program. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 37% = 37/100 = 0.37

q = 1 - p = 1 - 0.37

q = 0.63

n = 10

a) P(x = 2)

Therefore,

P(x = 2) = 10C2 × 0.37^2 × 0.63^(10 - 2)

P(x = 2) = 45 × 0.1369 × 0.02481557803

P(x = 2) = 0.15

b) P(x>2) = 1 - P(x ≤ 2)

P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)

P(x = 0) = 10C0 × 0.37^0 × 0.63^(10 - 0) = 0.0098

P(x = 1) = 10C1 × 0.37^1 × 0.63^(10 - 1) = 0.058

P(x = 2) = 0.15

P(x ≤ 2) = 0.0098 + 0.058 + 0.15 = 0.22

P(x>2) = 1 - 0.22 = 0.78