Advertisements
Advertisements
प्रश्न
If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week
Advertisements
उत्तर
In a poisson distribution
Mean (λ) = `3/20` = 0.15
P(X = x) = `("e"^(-lambda) lambda^x)/(x!)`
P(not be more than one failure) = P(X ≤ 1)
P(X = 0) + P(X = 1)
= `("e"^(-0.15) (0.15)^0)/(0!) + ("e"^(-0.15) (0.15)^1)/(1!)`
= `"e"^(-0.15) [(0.15)^0/(0!) + (0.15)^1/(1!)]`
= `"e"^(-0.15) [1 + 0.15]`
= `"e"^(-0.15) [1.15]`
= 0.86074 × (1.15)
= 0.98981
APPEARS IN
संबंधित प्रश्न
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes
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?
Consider five mice from the same litter, all suffering from Vitamin A deficiency. They are fed a certain dose of carrots. The positive reaction means recovery from the disease. Assume that the probability of recovery is 0.73. What is the probability that atleast 3 of the 5 mice recover
The average number of phone calls per minute into the switchboard of a company between 10.00 am and 2.30 pm is 2.5. Find the probability that during one particular minute there will be no phone at all
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 than 2,150 hours
If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have height greater than 72 inches
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:
In a large statistics class, the heights of the students are normally distributed with a mean of 172 cm and a variance of 25 cm. What proportion of students is between 165cm and 181 cm in height?
Choose the correct alternative:
Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be:
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?
