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**QUESTION **

A manufacturing plant operates on a three-shift system: Shift A, Shift B, and Shift C. The table below shows the number of units produced during each shift for two different products, Product X and Product Y.

Items

Shift

Product X

Product Y

A

90

30

B

65

45

C

55

70

Find the probability if getting Product X.

A Product Y was detected by the quality controller, find the probability it was produced during Shift A.

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**QUESTION 2**

The following is the probability distribution of the number of customers buying bicycle accessories at a particular shop in one day.

0

1

2

3

4

5

6

0.05

0.10

0.15

0.25

0.30

0.05

Compute the value of .

Find the probability that the shop did not sell any bicycle accessory in one day.

Find the probability that at least three customers bought from the shop in one day.

Find the probability that at most five customers bought from the shop in one day.

Find the expected value of .

Find the variance and standard deviation of .

(14 marks)

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**QUESTION 3**

A machine produces parts of which 8% are defective. If a random sample of 10 parts produced by this machine contains two or more defectives, the machine is shut down for repairs. Find the probability that the machine will be shut down based on this sampling plan.

(4 marks)

**QUESTION 4**

The number of students coming in complaining of stomach problems during a typical day at the Student Health Center is Poisson distributed with mean . If the probability that no student comes in complaining of stomach problems in one day is 0.015.

Calculate .

Find the probability that more than 6 students come in complaining of stomach problems in 2 days.

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