Respuesta :
Answer:
0.064 = 6.4% probability that none of the 10 calls result in a reservation.
Step-by-step explanation:
For each call, there are only two possible outcomes. Either it results in a reservation, or it does not. The probability of a call resulting in a reservation is independent of other calls. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
24% of the calls to an airline reservation phone line result in a reservation being made.
This means that [tex]p = 0.24[/tex]
Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls result in a reservation?
This is P(X = 0) when n = 10. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.24)^{0}.(0.76)^{10} = 0.064[/tex]
0.064 = 6.4% probability that none of the 10 calls result in a reservation.
