Math week , chap Mohoammed Mazheruddin Siddiqui



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Math week 2

Math week 2 , chap 3
Mohoammed Mazheruddin Siddiqui

3.15. An automated egg carton loader has a 1% probability of cracking an egg, and a customer will complain if more than one egg per dozen is cracked. Assume that each egg load is an independent event.


What is the distribution of cracked eggs per dozen? Include parameter values.
What is the probability that a carton of a dozen eggs results in a complaint?
What are the mean and standard deviation of the number of cracked eggs in a carton of a dozen eggs?

Ans:


  1. {n,p} with n = 12 and p = 0.015

  2. P(X > 1) = 1 (12 0) p 0 (1 - p) 12-0 –(12 1) p 1 (1 -p) 11 = 1 –(0.8341320 -12)× (0.015)× (0.985)11

= 0.0134

  1. σ= √np (1-p) = √12×0.015×0.985 = 0.4210

3.28 A manufacturer of a consumer electronics product expects 2% of units to fail during the warranty period. A sample of 500 independent units is tracked for warranty performance.


What is the probability that none fails during the warranty period?
What is the expected number of failures during the warranty period?
What is the probability that more than two units fail during the warranty period?

Ans:
Binomial Problem with n = 500 and p(fail) = 0.02 and P(good) = 0.98



  1. P(x = 500) =[500 0 ]× [0.002]0 ×0.98^500 = 0.000041024

  2. E(x) = np = 500*0.02 = 10

  3. P(x >=2) = 1 - P(x <2) = 0.995

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