Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes
Define Standard normal variate
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
Choose the correct alternative:
Normal distribution was invented by
Choose the correct alternative:
Which of the following statements is/are true regarding the normal distribution curve?
Choose the correct alternative:
The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of ₹ 180,000 and a standard deviation of ₹ 10,000. What is the probability that a randomly selected newly qualified CA will earn between ₹ 165,000 and ₹ 175,000?
Vehicles pass through a junction on a busy road at an average rate of 300 per hour. Find the probability that none passes in a given minute
Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Raghul wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Raghul takes the test and scores 585. Will he be admitted to this university?
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 between $45,000 and $65,000?
