Question

It is estimated that 0.5 percent of the callers to the Customer Service department of Dell, Inc. will receive a busy signal. What is the probability that of today's 1,200 callers at least 5 received a busy signal?

Name: Problem 29, Chapter 6: Basic Statistics for Business and Economics
Uploaded: 2022-01-09T17:41:55-08:00
Duration: 2 min 28 s
Channel: Robin Corrigan
Description: It is estimated that 0.5 percent of the callers to the Customer Service department of Dell, Inc. will receive a busy signal. What is the probability that of today's 1,200 callers at least 5 received a busy signal?

   It is estimated that 0.5 percent of the callers to the Customer Service department of Dell, Inc. will receive a busy signal. What is the probability that of today's 1,200 callers at least 5 received a busy signal?

Basic Statistics for Business and Economics

Douglas A. Lind,… 5th Edition

Chapter 6, Problem 29

Instant Answer

Solved by Expert Robin Corrigan

01/09/2022

Step 1

The mean is given by the product of the probability of an event occurring and the number of trials. In this case, the probability of a caller receiving a busy signal is 0.5% or 0.005, and the number of callers is 1200. Therefore, the mean is calculated as Show more…

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It is estimated that 0.5 percent of the callers to the Customer Service department of Dell, Inc. will receive a busy signal. What is the probability that of today's 1,200 callers at least 5 received a busy signal?

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Key Concepts

Poisson Approximation

The Poisson approximation is used to approximate the binomial distribution when the number of trials is large and the probability of success is small. In such cases, the binomial probability calculations become complex, and the Poisson distribution with a mean equal to np offers a simpler alternative.

Binomial Distribution

The binomial distribution models the number of successes in a fixed number of independent trials where each trial has only two possible outcomes and the probability of success remains constant. It is used to calculate probabilities when looking at a fixed number of repeated experiments.

Complement Rule

The complement rule is a probability principle stating that the probability of an event occurring is equal to one minus the probability that it does not occur. It is particularly useful for calculating cumulative probabilities by subtracting from one the probability of the event's complement.

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