Question

An online customer service department estimates that about 15 percent of callers have to wait more than 8 minutes to have their calls answered by a person. The department conducted a simulation of 1,000 trials to estimate the probabilities that a certain number of callers out of the next 10 caliers will have to wait more than 8 minutes to have their calls answered. The simulation is shown in the following histogram.
A)0.150
B)0.190
C)0.474
D)0.526
E)0.810

Answer 1

Answer:

E). 0.810

Explanation:

The simulation displayed through the histogram shows that the probability of getting 'at most 2 of the next 10 callers who will have to wait more than 8 minutes to get their calls answered' would be 0.810.

= P(x ≥ 2) = P(0) + P(1) + P(2)

= 0.181 + 0.345 + 0.284

= 0.810

Answer 2

The probability that at most 2 of the next 10 callers have to wait more than 8 minutes is the sum of the probabilities of 0, 1 or 2 callers having to wait for more than 8 minutes which is 0.810

The probability that at most 2 of the next 10 callers having to wait can be defined using the expression :

P(X ≤ 2) = P(0) + P(1) + P(2)

Using the individual probabilities given by the histogram attached :

P(X ≤ 2) = 0.181 + 0.345 + 0.284

P(X ≤ 2) = 0.810

Therefore, the probability that at most 2 callers have to wait more than 8 minutes is 0.810

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