Question: "According to sales information in the first quarter..."

chillywilly12a

Answered question

2021-09-17

According to sales information in the first quarter of 2016. 2.5% of new vehicles sold in the United States were hybrids. This is down from 2.8% for the same period a year earlier. An analysts

Answer & Explanation

oppturf

Skilled2021-09-18Added 94 answers

Step 1
Given data
No of vehicles $(n) = 35$
Probability that the new car sales is hybrid $(p) = 0.025$
a) Expected no of vehicles would be hybrid is given by
$m e a n = n p = 35 \times 0.025 = 0.875 \tilde{=} 1$
Because no of vehicles always be in positive integer
b) In poisson distribution mean is given
$μ = n p = 35 \times 0.025 = 0.875$
Let X represents no of hybrid vehicles
X follows poisson distribution with mean 0.875
Probability density function of poisson distribution is given by
$P (X = x) = \frac{e^{- μ} \times μ^{x}}{x!}$
Probability that the four of the sales were hybrid vehicles is given by
$P (X = 4) = \frac{e^{- 0.875 \times {0.875}^{4}}}{4!} = 0.0102$
Step 2
c) Now using binomial distribution
Probability that the four of the sales were hybrid vehicles is given by
Applying Binomial theorem
Probability of x success out of n trial is given by
$P (X = x) = (b e g \in {a r r a y} {c} n ∖ x e n d {a r r a y}) \times p^{x} \times {(1 - p)}^{n - x}$
$\Rightarrow P (X = 4) = (b e g \in {a r r a y} {c} 15 ∖ 4 e n d {a r r a y}) \times {0.025}^{4} \times {(1 - 0.025)}^{35 - 4}$
$= \frac{35!}{4! \times (31 - 4)!} \times {0.025}^{4} \times {(1 - 0.025)}^{35 - 4}$
$\Rightarrow 0.0093$
Step 3
Answers
a)1
b) 0.0102
c) 0.0093

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