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∑ A_kP_k(x)

k=0

∫0 to 2π{dθ/](3+2cosθ)}

1. ln(z+3i)/z^2

2. z^2-2z/(z^2+2z+2)

P (Company will pass test/no shortage) = 0.90

P (Company will pass test/small shortage) = 0.50

P (Company will pass test/large shortage) = 0.20

Required:

i) Determine the probability if a company being audited fails this test has large or small inventory shortage.

ii) If a company being audited passes this test, what is the probability of no inventory shortage?

X 1 2 3 4 5

Y 2 5 3 8 7

Assume a normal distribution.

i) How many lamps will fail before 900 hours?

ii) How many lamps will fail between 950 and 1000 hours?

iii) What proportion of lamps will fail before 925 hours?

iv) Given the same mean life, what would the standard deviation have to be to ensure that no more than 20% of lamps fail before 916 hours