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A cell phone manufacturer has noticed that the number of faulty cell phones detected in a...

A cell phone manufacturer has noticed that the number of faulty cell phones detected in a production run only depends on the supervisor on duty and is detected according to a Poisson Process. There are only 2 supervisors: James and Russell, in the firm. The average number of faulty cell phones is two per day when James is on duty, while the average number of faulty cell phones is three per day when Russell is on duty. It is also known that the quality of one day’s production doesn’t seem to have bearing on the next day. Russell works 3 out of 5 days, while James works 2 out of 5 days.

  1. a) (2) What is the probability that no faulty cell phones will be produced tomorrow, if Russell is on duty?
  2. b) (1) What is the expected number of faulty cell phones to be produced in the next two days, if Russel is on duty?
  3. c) (3) What is the probability that no faulty cell phones will be produced in the next two days?
  4. d) (4) Suppose at least one faulty cell phone was produced yesterday, what is the probability that James was on duty?
math   Statistics-And-Probability   
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Answer #1

b)Expected number=3*2=6 faulty cell phones

c)P(0 phones)=P(2days Russel)*P(0 phones|2 days Russel)+P(2days James)*P(0phones|2 days James)+P(1day russel, 1day james)*P(0 phones|1day James,1day Russel)

d)P(atleast one faulty phone|Russel)=1-P(no faulty line|Russel)=

P(atleast one faulty phone|James)=1-P(no faulty line|James)=

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