Advertisements
Advertisements
Question
A car hiring firm has two cars. The demand for cars on each day is distributed as a Posison variate, with mean 1.5. Calculate the proportion of days on which some demand is refused
Advertisements
Solution
In a Poisson distribution n = 2
Mean λ = 1.5
x follows a Poisson distribution
With in P(x) = `(e^(-lambda) lambda^x)/(x!)`
P(some demand is refused) = P(X > 2)
= 1 − P(X ≤ 2)
= 1 − [P(X = 0) + P(X = 1) + P(X = 2)]
= `1 - [(e^(-1.5) (1.5)^0)/(0!) + (e^(-1.5) (1.5)^1)/(1!) + (e^(-1.5) (1.5)^2)/(2!)]`
= `1 - e^(-1.5) [(1.5)^0/(0!) + (1.5)^1/(1!) +(1.5)^2/(2!)]`
= `1 - e^(-1.5) [1 + .5 + 2.25/2]`
= 1 – 0.2231 [1 + 1.5 + 1.125]
= 1 – 0.2231 [3.625]
= 1 − 0.8087
= 0.1913
APPEARS IN
RELATED QUESTIONS
If 5% of the items produced turn out to be defective, then find out the probability that out of 20 items selected at random there are atleast two defectives
Among 28 professors of a certain department, 18 drive foreign cars and 10 drive local made cars. If 5 of these professors are selected at random, what is the probability that atleast 3 of them drive foreign cars?
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that 12 of the travelers will not have a laptop?
Define Normal distribution
Choose the correct alternative:
Normal distribution was invented by
Choose the correct alternative:
Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?
Choose the correct alternative:
If P(Z > z) = 0.5832 what is the value of z (z has a standard normal distribution)?
A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain at least 2 rejects?
Vehicles pass through a junction on a busy road at an average rate of 300 per hour. What is the expected number passing in two minutes?
The birth weight of babies is Normally distributed with mean 3,500g and standard deviation 500g. What is the probability that a baby is born that weighs less than 3,100g?
