Question

Approximately 16% of the calls to an airline reservation phone line result in a reservation being made. (a) Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls result in a reservation? (Give the answer to 3 decimal places.) (b) What assumption did you make to calculate the probability in Part (a)? Calls are independent. Calls are dependent. (c) What is the probability that at least one call results in a reservation being made? (Hint: Use your answer to Part (a). Give the answer to 3 decimal places.)

Answer 1

Solution:

p = 16% = 0.16

(a )

n = 10 , Using Binomial distribution,

Probability Mass Function for Binomial Distribution, P(X = x) = (*) p*(1 – p)-1 x = 0,1,2, ..., n Here, n n! x!(n - x)! n!= n*(n-1) * * 1 .... for x = 0

for x = 0 P(X = 0) = (6) -0.16*(1 – 0.16 ) 10-0 = 0.1719

Answer : 0.1749

(b )

• Calls are independent.

(c )

P(at least one call results in a reservation) = 1 - P( x = 0 ) = 1 - 0.1749 = 0.8251

Answer : 0.8251