Question 1206340: 21% 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.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! p = the probability that they use the credit cards because of the rewards program.
q = 1 - p = the probability that they don't use the credit cards because of the rewards program.
binomial probability distribution is used for this.
n = 10 = total number of possible choices.
x = 0 to 10 = the number of students who are using the credit card because of the rewards program.
p = .21
q = 1 - p = .79
find the probability that (a) exactly two, (b) more than two, (c) between two and five inclusive, use the credit cards for the rewards program.
for (a), you want p(x) for x = 2.
for (b), you want p(x) for x > 2.
for (c), you want p(x) for x = 2 to 5 inclusive.
i used excel to do the calculations.
they are shown below:
problems are shown below.
find the probability that (a) exactly two, (b) more than two, (c) between two and five inclusive, use the credit cards for the rewards program.
answers to the problems are shown below.
p(x) for x = 2 is equal to 0.301070243.
p(x) for x > 2 is equal to 0.352558644.
p(x) for x = 2 to 5 inclusive is equal to 0.64543536.
the binomial probability formula is p(x) = p^x * q^(n-x) * c(n,x).
for example:
p(x = 2) is equal to .21^2 * .79^(10-2) * c(10,2) = .21^2 * .79^8 * 45 = .3010702433.
this agrees with the excel calculation when you round to the same number of decimal digits.
c(10,2) = 10! / (2! * 8!) = (10 * 9 * 8!) / (2! * 8!) = (10 * 9) / 2 = 45.
the general formula for c(n,x) is n! / (x! * (n-x)!)
|
|
|
