Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 5.9 percent and the standard deviation was 10.5 percent. a. What is the probability that your return on this asset will be less than –7.3 percent in a given year? Use the NORMDIST function in Excel® to answer this question. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What range of returns would you expect to see 95 percent of the time? (Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c. What range of returns would you expect to see 99 percent of the time?

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and

corporate bond fund, and the third is a T-bill money market fund

that yields a sure rate of 5.5%. The probability distributions of the

risky funds are:

The correlation between the fund returns is 0.15.

What is the Sharpe ratio of the best feasible CAL?

#first find the weights (Ws, Wb) for the stocks and bonds

#then after the weights for the optimal portfolio (i.e. highest Sharpe ratio/steepest part of CAL) → use Rule two to find the expected return of the portfolio and rule 3 to find std. Dev.

→ then find the sharpe ratio of these values to get the optimal risky portfolio (Steepest CAL tangent with the investment opp. Set).

Suppose you are interested in how long it takes to get your food at a restaurant. Now, suppose this distribution is approximately normal with an average of eight minutes and a standard deviation of two minutes. If you made a control chart for this data, what would be the highest control limit? Using the above scenario, suppose someone gets the food after exactly eleven minutes. How many standard deviations from the mean is this value of eleven? Using the above scenario, what is the probability that someone would get the food after more than eleven minutes?

[I know the answer involves P(X>11) = P(X>1.5) = 0.5-0.4332 = 0.0668, what I don't understand is how you get the values of P(X>11) or P(X>1.5) or where 0.4332 comes from]

The probability of A is 0.7, the probability of B is 0.8. What are the possible values for the probability of both A and B happening?

1. The probability of a student playing basketball is known to be 0.53; and the probability of a student playing soccer is known to be 0.43. If the probability of playing both is known to be 0.35, calculate:
   1. the probability of playing soccer
   2. the probability of playing at least one of basketball and soccer
   3. the probability of a student playing soccer, given that they play basketball?
   4. Are playing soccer and basketball independent? Justify
   5. (harder) a group of 29 randomly selected students attend a special seminar on the health benefits of playing sport. Of these 29, only 6 play neither after the seminar. State a sensible null hypothesis, test it, and interpret.

If the probability that a bowler will bowl a strike is 0.7, what is the probability that he will get exactly four strikes in eight attempts? At least four strikes in eight attempts? (Assume that the attempts to bowl a strike are independent of each other. Round your answers to three decimal places.)

exactly four strikes

at least four strikes

There is a 28.10% probability of a below average economy and a 71.90% probability of an average economy. If there is a below average economy stocks A and B will have returns of -7.40% and 18.50%, respectively. If there is an average economy stocks A and B will have returns of 11.50% and -0.80%, respectively. Compute the:

a) Expected Return for Stock A :

The probability of a student playing football is known to be 0.53; and the probability of a student playing rugby is known to be 0.5. If the probability of playing both is known to be 0.38, calculate:

(a) the probability of playing rugby

(b) the probability of playing at least one of football and rugby

(c) the probability of a student playing rugby, given that they play football

(d) Are playing rugby and football independent? Justify

(e) (harder) a group of 29 randomly selected students attend a special seminar on the health benefits of playing sport. Of these 29, only 5 play neither after the seminar. State a sensible null hypothesis, test it, and interpret.

Notes:
• Show detailed working, including appropriate mathematical notation for each question. For most questions this will involve showing your working from R Studio, (e.g. cut-and-paste commands and output from an R session).

• Any question involving regression will score 0 marks unless a scattergraph is produced.

•No Additional Info provided

Match the described probability with the type of probability.