Advertisements
Advertisements
प्रश्न
A car hiring firm has two cars. The demand for cars on each day is distributed as a Poison variate, with mean 1.5. Calculate the proportion of days on which some demand is refused
उत्तर
In a posion distribution n=2
Mean λ = 1.5
x follows poison 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
संबंधित प्रश्न
Defects in yarn manufactured by a local mill can be approximated by a distribution with a mean of 1.2 defects for every 6 metres of length. If lengths of 6 metres are to be inspected, find the probability of less than 2 defects
If 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random atmost 2 will be defective
The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution
The distribution of the number of road accidents per day in a city is poisson with mean 4. Find the number of days out of 100 days when there will be no accident
The distribution of the number of road accidents per day in a city is poisson with mean 4. Find the number of days out of 100 days when there will be atleast 2 accidents
Choose the correct alternative:
The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are
Choose the correct alternative:
Using the standard normal table, the sum of the probabilities to the right of z = 2.18 and to the left of z = – 1.75 is
Choose the correct alternative:
In a binomial distribution, the probability of success is twice as that of failure. Then out of 4 trials, the probability of no success is
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 no more than 2 rejects?
The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. What percent of people earn more than $75,000
