Question

There is an 85% chance that a randomly selected person will take their own re - usable bags to the grocery store.

a. If 20 shoppers are randomly selected, what is the mean and standard deviation for the number of people what will use their own re- usable bags at the grocery store?

b. If 20 shoppers are randomly selected what is the probability that at most 9 shoppers will use their own re - usable bags at the grocery store?

c. If 20 shoppers are randomly selected what is the probability that at least 5 shoppers will use their own re - usable bags at the grocery store?

Answer 1

here this is binomial distribution with parameter n=20 and p=0.85

a) mean =np=20*0.85 =17

std deviation =sqrt(np(1-p))=1.5969

b)

probability that at most 9 shoppers will use their own re - usable bags at the grocery store =P(X<=9)

= =0.000039

c)

probability that at least 5 shoppers will use their own re - usable bags at the grocery store =P(X>=5)=1-P(X<=4)

=1- =1- 0.000000~ 1.000000