Advertisements
Advertisements
Question
The average number of customers, who appear in a counter of a certain bank per minute is two. Find the probability that during a given minute three or more customers appear
Advertisements
Solution
The average number of customers
Who appear in a counter of a certain bank per minute = 2
∴ λ = 2
x follows poisson distribution with P(x) = `("e"^(-lambda)lambda^x)/(x!)`
P(three or more customers appears) = P(X ≥ 3)
= P(X = 3) + P(X = 4) + P(X = 5) + ……
= 1 – P(X < 3)
= 1 – {P(X = 0) + P(X = 1) + P(X = 2)}
= `1 - {("e"^-1(2)^0)/(0!) , ("e"^-1(2)^2)/(1!), ("e"^-2(2)^2)/(2!)}`
= `1 "e"^-2 [1 + 2 + 4/2]`
= 1 – 2-2 [1 + 2 + 2]
= 1 – 0.1353(5)
= 1 – 0.6765
= 0.3235
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
If the probability of success is 0.09, how many trials are needed to have a probability of atleast one success as 1/3 or more?
Assume that a drug causes a serious side effect at a rate of three patients per one hundred. What is the probability that atleast one person will have side effects in a random sample of ten patients taking the drug?
The average number of customers, who appear in a counter of a certain bank per minute is two. Find the probability that during a given minute no customer appears
Define Normal distribution
In a test on 2,000 electric bulbs, it was found that bulbs of a particular make, was normally distributed with an average life of 2,040 hours and standard deviation of 60 hours. Estimate the number of bulbs likely to burn for more 1,920 hours but less than 2,100 hours
Choose the correct alternative:
If for a binomial distribution b(n, p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to
Choose the correct alternative:
If the area to the left of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?
Choose the correct alternative:
If P(Z > z) = 0.8508 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 no more than 2 rejects?
