English
Tamil Nadu Board of Secondary EducationHSC Commerce Class 12

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 failu

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

Sum
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

shaalaa.com
Distribution
  Is there an error in this question or solution?
Chapter 7: Probability Distributions - Miscellaneous problems [Page 171]

APPEARS IN

Samacheer Kalvi Business Mathematics and Statistics [English] Class 12 TN Board
Chapter 7 Probability Distributions
Miscellaneous problems | Q 3 | Page 171

RELATED QUESTIONS

Mention the properties of binomial distribution.


In a particular university 40% of the students are having newspaper reading habit. Nine university students are selected to find their views on reading habit. Find the probability that atleast two-third have newspaper reading habit


Define Poisson distribution


Define Normal distribution


In a distribution 30% of the items are under 50 and 10% are over 86. Find the mean and standard deviation of the distribution


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 between 65 and 71 inches


Choose the correct alternative:

The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84?


Choose the correct alternative:

A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls lasts less than 180 seconds?


Choose the correct alternative:

Cape town is estimated to have 21% of homes whose owners subscribe to the satellite service, DSTV. If a random sample of your home is taken, what is the probability that all four homes subscribe to DSTV?


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?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×