a) Compute the number of vehicles expected to be hybrid. b)

Tammy Todd

Tammy Todd

Answered question

2021-09-17

a) Compute the number of vehicles expected to be hybrid.
b) Compute the probability that five of the sales were hybrid vehicles using Poisson distribution.
c) Compute the probability that five of the sales were hybrid vehicles using binomial distribution.

Answer & Explanation

Roosevelt Houghton

Roosevelt Houghton

Skilled2021-09-18Added 106 answers

a) The mean and variance of success in Poisson distribution are same. Its formula is as follows:
μ=nπ
where, n is the total number of trials and π is the probability of success
Here, n is 40 and π is 0.027.
The number of vehicles expected to be hybrid is calculated as follows:
μ=40×0.027
=1.08
Thus, the number of vehicles expected to be hybrid is 1.08.
b) Poisson distribution:
The number of times an event occurs during a given interval is described by Poisson distribution. The mathematical formula for Poisson distribution is as follows:
P(x)=μxeμx!
where, μ is the average number of occurrences in an interval,
e=2.71828
x is the number of occurrences
P(x) is the probability for a specific value
The Poisson probability that five of the sales were hybrid vehicles is calculated as follows:
P(5)=1.085e1.085!
=0.4990120
=0.0042
Therefore, the Poisson probability that five of the sales were hybrid vehicles is 0.0042.
c) The formula to find the binomial probability is as follows:
P(X)=nCxπx(1π)(nx)
where, C is the combination.
n is the number of trials.
X is the random variable.
π is the probability of success.
The binomial probability that five of the sales were hybrid vehicles is calculated as follows:
P(x=5)=40C5(0.027)5(10.027)(405)
=40!5!(405)!×0.0275×0.97335
=0.0036
Therefore, the binomial probability that five of the sales were hybrid vehicles is 0.0036.

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