It has been found that on average, 7 cars use a garage in any given 10‐minute period. What is the probability that: Q.2.2.1 Four cars will use the garage in any given five‐minute period? Interpret your answer. Q.2.2.2 Less than two cars will use the garage in any given 10‐minute period? Interpret your answer. Q.2.2.3 More than two cars will use the garage in any given 10‐minute period? Interpret your answer

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 44E
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It has been found that on average, 7 cars use a garage in any given 10‐minute period. What is the probability that:

Q.2.2.1 Four cars will use the garage in any given five‐minute period? Interpret your answer.

Q.2.2.2 Less than two cars will use the garage in any given 10‐minute period? Interpret your answer.

Q.2.2.3 More than two cars will use the garage in any given 10‐minute period? Interpret your answer.

Expert Solution
Step 1

A random variable X is called to follow the Poisson distribution if its takes only non-negative values and its probability mass function is given by:

P(X=x)=e-λλxx!; x=0,1,...; λ>0

Here λ  is the parameter of the distribution. It is denoted as X~Poisson(λ). For Poisson distribution, the mean and variance both are equal to λ. It is used when the events do not occur as the outcomes of a definite number of trials of an experiment but occur at random points of time and space.

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