Q1.A disease has a 6% prevalence in the population. You need to choose between two tests.

If the disease is present, thefirst test will give a positive result with probability 0.90. If the disease is not present, it will give a positive result with probability 0.07. If the disease is present, thesecond test will give a positive result with probability 0.96. If the disease is not present, it will give a positive result with probability 0.10.

1. For each of the tests, what is the probability that someone has the disease given a positive test result?

1. The disease is highly contagious, and so those with the disease need to be quarantined. Which testwould you recommend? Explain your reasoning.

Q2. An investment firm has classified its clients according to their gender and the composition of their investment portfolios (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Portfolio Composition

Gender	Bonds	Stocks	Balanced
Male	0.18	0.20	0.25
Female	0.12	0.10	0.15

One client is selected at random, and two events A and B are defined as follows:

A: The client selected is male.

B: The client selected has a balanced portfolio.

Find the following probabilities.

1. P(A).
2. P(B).
3. P(A|B)

Q3. A telephone receptionist takes an average of six calls per hour. Calculate the probability that the receptionist takes:

1. exactly five calls in the next 45 minutes.
2. two or more calls in the next 30 minutes.

Q4. Consideraninvestmentwhosereturnisnormally distributedwithameanof 10% and a standard deviation of 5%.

1. Please determinetheprobabilityoflosingmoney.

2. Considerasituation wherethestandard deviationincreasesto10%.Please determine the probability of losing money.

Q5. In the first quarter of 2014, the rental cost of a three-bedroom house in a regional town was $300 with a standard deviation of $30. Assume that the rental costs are normally distributed. If you select a random sample of ten rental properties, what is the probability that the sample willhave a mean rental cost of:

1. Less than $275?

1. Between $280 and $300?

1. Greater than $310?