Mathematics: Approximately 17% 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.)

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Approximately 17% of the calls to an airline

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22.01.2022

Probability that none of the 10 calls result in a reservation =

P(X = 0) = 0.155

Step-by-step explanation:

Given

The probability of calls to an airline reservation phone line result in a reservation being made = p = $\frac{17}{100}$ =0.17

The probability of calls to an airline reservation phone line result in a reservation is not done = q = 1 - p = 1 - 0.17 = 0.83

Suppose that an operator handles 10 calls

n = 10

probability that none of the 10 calls result in a reservation

( Using binomial distribution)

Let X be number of calls being reserved

P(X = 0) = $\binom{n}{r}p^{r}q^{n - r}$

= $\binom{10}{0}(.17)^{0}(.83)^{10 - 0}$

= $(.83)^{10}$

= 0.155

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