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 A car hire firm has 2 cars which is hired out everyday. The number of demands per day for a car follows Poisson distribution with mean 1.20. What is the proportion of days on which some demand is refused?(Given e 1.20 = 3.32).

  • a)
    0.25

  • b)
    0.3012

  • c)
    0.03

  • d)
    0.12

Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A car hire firm has 2 cars which is hired out everyday. The number of ...
P(x)  = λˣ  e^(-λ) / x!
Mean demand =   λ = 1.2
Demand is not refused if demand  is 0 , 1 or  2
Demand is refused if more than 2
Demand is not refused = P(0) + P(1) + P(2)
= 1.2⁰ *  / 0!  + 1.2¹ *
=  0.301  +  0.3614  +  0.2169
= 0.8793  
Demand is refused  1  -  0.8793  =   0.1207
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A car hire firm has 2 cars which is hired out everyday. The number of ...
Given:
- A car hire firm has 2 cars which are hired out every day.
- The number of demands per day for a car follows Poisson distribution with mean 1.20.
- e¹.²⁰ = 3.32

To find: The proportion of days on which some demand is refused.

Solution:
Let X be the number of demands per day for a car.
Given, X follows Poisson distribution with mean 1.20.
Therefore, P(X = x) = e^(-1.20) * (1.20)^x / x!

We know that the firm has 2 cars available for hire. So, if the number of demands is less than or equal to 2, then all demands can be met. If the number of demands is greater than 2, then some demands will have to be refused.

Therefore, the proportion of days on which some demand is refused is given by:

P(X > 2) = 1 - P(X ≤ 2)
= 1 - [P(X = 0) + P(X = 1) + P(X = 2)]
= 1 - [e^(-1.20) * (1.20)^0 / 0! + e^(-1.20) * (1.20)^1 / 1! + e^(-1.20) * (1.20)^2 / 2!]
= 1 - [0.3012 + 0.3614 + 0.2168]
= 0.1206
≈ 0.12

Therefore, the proportion of days on which some demand is refused is 0.12 (option D).
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A car hire firm has 2 cars which is hired out everyday. The number of demands per day for a car follows Poisson distribution with mean 1.20. What is the proportion of days on which some demand is refused?(Given e1.20= 3.32).a)0.25b)0.3012c)0.03d)0.12Correct answer is option 'D'. Can you explain this answer?
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