Question

Doordash has campaigned that it gets 92.5% of the deliveries on time compared to UberEATS which has a delivery time of 88% and Postmate which has a delivery time of 91%. A food columnist decided to survey 14 customers of all three delivery companies:

a) What is the probability that at most half of the customers surveyed say that their Postmate orders were delivery on time? b) What is the probability that at least six of the respondents say that their Doordash orders were delivered on time? c) What is the probability that fewer than eight of the respondents say UberEATS delivered their food on time? d) What is the mean and standard deviation of the binomial distribution of all three delivery companies? HTML EditorKeyboard Shortcuts

Answer 1

p_D = Probability that Doordash delivers on time = 0.925

p_U = Probability that UberEATS delivers on time = 0.88

p_P = Probability that Postmate delivers on time = 0.91

n = Size of the sample = 14

X_D = Number of people that said Doordash delivered on time

X_U = Number of people that said UberEATS delivered on time

X_P = Number of people that said Postmate delivered on time

a)  What is the probability that at most half of the customers surveyed say that their Postmate orders were delivered on time?

= 0.0001

[Using R code pbinom(7,14,0.91)]

b) What is the probability that at least six of the respondents say that their Doordash orders were delivered on time?

= 0.9999999

[Using R code "1-pbinom(5,14,0.925)"]

c) What is the probability that fewer than eight of the respondents say UberEATS delivered their food on time?

= 0.00057

[Using R code "pbinom(7,14,0.88)"]

d) What is the mean and standard deviation of the binomial distribution of all three delivery companies?

E(X_D) = n . p_D = 14 x 0.925 = 12.95

E(X_U) = n . p_U = 14 x 0.88 = 12.32

E(X_P) = n . p_P = 14 x 0.91 = 12.74