Question

A large fast-food restaurant is having a promotional game where game pieces can be found on various products. Customers can win food or cash prizes. According to the company, the probability of winning a prize (large or small) with any eligible purchase is 0.192.

Consider your next 34 purchases that produce a game piece. Calculate the following:

This is a binomial distribution. Round your answers to 4 decimal places.

a) What is the probability that you win 7 prizes?

b) What is the probability that you win more than 9 prizes?

c) What is the probability that you win between 4 and 7 (inclusive) prizes?

d) What is the probability that you win 5 prizes or fewer?

Answer 1

here this is binomial with parameter n=34 and p=0.192

a)

P(X=7)=

(nCx)px(1−p)(n-x)    =

0.1637

if using ti-84 press -2nd -vars :binompdf(34,0.192,7)

if using excel use command :binomdist(7,34,0.192,false)

b)

P(X>=10)=1-P(X<=9)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.1016

if using ti-84 press 2nd -vars- command :1-binomcdf(34,0.192,9)

if using excel use command :1-binomdist(9,34,0.192,true)

c)

P(4<=X<=7)=

∑x=ab     (nCx)px(1−p)(n-x)    =

0.5909

if using ti-84 press 2nd -vars- command :binomcdf(34,0.192,7)-binomcdf(34,0.192,3)

if using excel use command :binomdist(7,34,0.192,true)-binomdist(3,34,0.192,true)

d)

P(X<=5)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.3412

if using ti-84 press 2nd- vars - command :binomcdf(34,0.192,5)

if using excel use command :binomdist(5,34,0.192,true)