Question

Suppose that you and two friends go to a restaurant which last month filled approximately 90.9% of the orders correctly.

a. What is the probability that all three orders will be filled correctly?

b. What is the probability that none of the three orders will be filled correctly?

c. What is the probability that at least two of the three orders will be filled correctly?

d. What are the mean and standard deviation of the binomial distribution used in a through d

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

P(order filled correctly), p = 0.909

q = 1 - 0.909 = 0.091

n = 3

a. P(all three orders will be filled correctly), P(3) = 0.909³

= 0.7511

b. P(none of the orders will be filled correctly), P(0) = 0.091³

= 0.0008

c. P(at least 2 of the three orders will be filled correctly) = P(2) + P(3)

= 3C2 x 0.909² x 0.091 + 0.909³

= 0.9767

d. Mean = np

= 3x0.909

= 2.727

Standard deviation =

=

= 0.4982