34% of college students say they use credit cards because of rewards program. Yo

ruigE

ruigE

Answered question

2021-09-18

34% of college students say they use credit cards because of 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 include. If convenient, use technology to find the probabilities.
(a)P(2)=?

Answer & Explanation

i1ziZ

i1ziZ

Skilled2021-09-19Added 92 answers

Step 1
Given:
34% of the students say they use credit cards because of rewards , p=0.34
sample size, n=10
Let X be the number of students out of sample saying they use credit cards because of rewards
X denotes the binomial distribution
The full binomial probability formula with the binomial coefficient is:
P(X)=n!X!(nX)!pX(1p)nX
Step 2
a) Probability Event =Pr(X=2)
This implies that:
Pr(X=2)=(102)0.342×0.66102
=0.1873
which means that the probability we are looking for is Pr(X=2)=0.1873
b) Probability Event=P(X>2)=Pr(X3)
Therefore, we get that:
Pr(X3)=i=310Pr(X=i)=i=310(ni)pi(1p)ni
This implies that
Pr(X3)=Pr(X=3)+Pr(X=4)+Pr(X=5)+Pr(X=6)+Pr(X=7)+Pr(X=8)+Pr(X=9)+Pr(X=10)
=(103)0.343×0.66103+(104)0.344×0.66104+(105)0.345×0.66105+(106)0.346×0.66106+(107)0.347×0.66107+(108)0.348×0.66108+(109)0.349×0.66109+(1010)0.3410×0.661010
=0.2573+0.232+0.1434+0.0616+0.0181+0.0035+0.0004+0
=0.7162
which means that the probability we are looking for is Pr(X>2)=0.7162
c) Probability Event =Pr(2X5)
Therefore, we get that
Pr(2X5)=i=25Pr(X=i)=i=25(ni)pi(1p)ni
This implies that

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