Question

2. A financial advisor informs a client that the expected return on a portfolio is 8% with a standard deviation of 12%. There is a 25% chance the return will be negative and a 15% chance that the return would be above 16%. Does her assessment follow a normal distribution? Calculate the probabilities for a normal distribution and compare. 3. A new water filtration system is sold with a 10-year warranty that includes all parts and repairs. Suppose the life of the system has a mean of 16 years and a standard deviation of 5 years. a. What is the probability that the water filtration system will require repair during the warranty period? b. Supposed the firm makes $300 profit for every new system it installs. This profit, however, is reduced to $50 if the system requires repair during the warranty period. Find the expected profit of the firm if it installs 1,000 new water filtration systems.

Answer 1

Answer)

3)

As the population s.d is given we can use standard normal z table to estimate the answer

Z = (x-mean)/s.d

Given mean = 16

S.d = 5

A)

Filtration system will require warranty repair if, x< 10

P(x<10)

Z = (10 - 16)/5

Z = -1.2

From z table, p(z<-1.2) = 0.1151

Required probability is 0.1151

B)

Probability that a system requires repairing = 0.1151

So total number of systems which requires repairing = 0.1151*1000 = 115.1

Profit when a system requires repair = 300-50 = $250

And profit when a system does not require repair = $300

Profit for 115.1 (systems which requires repair) = 28775 (115.1*250)

Profit for 1000 - 115.1 = 884.9 (systems which does not require repair) =

265470

Total expected profit = 265470 + 28775

= $294245