22% of college students say they use credit cards because of the rewards program

Question

22% 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, and (c) between two and five inclusive. If convenient, use technology to find the probabilities. P(2) = _ (Round to the nearest thousandth as needed. P(x > 2) = _ (Round to the nearest thousandth as needed. P(2 lessthanorequalto x lessthanorequalto 5) = _ (Round to the nearest thousandth as needed.)

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a)
P( X = 2 ) = ( 10 2 ) * ( 0.22^2) * ( 1 - 0.22 )^8
= 0.2984
b)
P( X < 2) = P(X=1) + P(X=0) +
= ( 10 1 ) * 0.22^1 * ( 1- 0.22 ) ^9 + ( 10 0 ) * 0.22^0 * ( 1- 0.22 ) ^10 +   
= 0.3185
P( X > = 2 ) = 1 - P( X < 2) = 0.6815
c)
P( X = 3 ) = ( 10 3 ) * ( 0.22^3) * ( 1 - 0.22 )^7
= 0.2244
P( X = 4 ) = ( 10 4 ) * ( 0.22^4) * ( 1 - 0.22 )^6
= 0.1108
P( X = 5 ) = ( 10 5 ) * ( 0.22^5) * ( 1 - 0.22 )^5
= 0.0375
P(2<=X<=5) = P( X = 2 ) + P( X = 3 ) + P( X = 4) + P( X = 5) =
       = 0.2984 + 0.2244 + 0.1108 + 0.0375
       = 0.6711

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.