A new shopping mall is considering setting up an information desk manned by one employee. Based upon data obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 15 per hour. It takes an average of 1.5 minutes to answer a question. It is assumed that the arrivals are Poisson and answer times are exponentially distributed.

What is the probability that the service facility will be idle?

What is the average time (hours) a customer spends getting information?

What is the average number of customers in the system?

What is the probability an arriving customer has to wait?

Three barbers work at a barbershop. Based on estimations, the barbershop is idle 1 time out of 15; 2/15 of the time there is one customer; 3 times out of 15 there are two customers; and 4/15 of the time, there are three customers. Each customer yields a net revenue of 10 dollars.

Let X be a random variable defined as the number of customers

a) Determine the probability distribution of X

b) Determine the cumulative distribution function of X

c) Calculate the probability that: i) All three barbers are working. ii) At least one of the barbers is working

The arrival of flights ar DIA has been monitored for the last year. From the research, 65.17 % of all arrivals are on time. Suppose a random sample of 16 flight arrivals is examined.
Using the binomial function,answer the following questions.

1. Create a table and enter only the first and last value in that table.

2. Give the probability of exactly 10 on time arrivals?


3. Give the probability of at most 9 on time arrivals?


4. Give the expected (mean) mean number of on time arrivals.

a) In a small country, the probability that a person will die from a certain respiratory infection is 0.004. Let ? be the random variable representing the number of persons infected who will die from the infection. A random sample of 2000 persons with this disease is chosen.

(i) Determine the exact distribution of ? and state TWO reasons why it was chosen? [4 marks]

(ii) State the values of ?(?) and ???(?). [2 marks]

(iii) Using a suitable approximate distribution, find the probability that fewer than 5 persons will die from the infection. (Do not use the exact distribution in part (i)). [4 marks]

Suppose that the price of a share of a particular stock listed on the New York Stock Exchange is currently $39. The following probability distribution shows how the price per share is expected to change over a three-month period: Stock Price Change ($) Probability –2 0.05 –2 0.10 0 0.25 +1 0.20 +2 0.20 +3 0.10 +4 0.10 (a) Construct a spreadsheet simulation model that computes the value of the stock price in 3 months, 6 months, 9 months, and 12 months under the assumption that the change in stock price over any three-month period is independent of the change in stock price over any other three-month period. For a current price of $39 per share, what is the average stock price per share 12 months from now? What is the standard deviation of the stock price 12 months from now? Round your answers to two decimal places. Average $ 43 Standard Deviation $ 4 (b) Based on the model assumptions, what are the lowest and highest possible prices for this stock in 12 months? Minimum $ 32 Maximum $ 55 Based on your knowledge of the stock market, how valid do you think this is? Propose an alternative to modeling how stock prices evolve over three-month periods. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank

1. Rank the following interest rates from lowest to the highest and identify it is a source (S) or use (U) of capital. If it is both a source and use of capital, then state both (B)

   • - Federal Funds Rate (FFR)

   • - LIBOR

   • - Interest on Reserves (IOR)

   • - Discount Rate (DR)

   • - Prime Rate

   • - Risk Free Rate

   • - Reverse Repurchase Agreements (Repos)

The highest and lowest birth rates in the United States in 2010 were in Utah and Maine, respectively. Utah reported 52,258 births with a population of about 2.8 million people. Maine reported 12,970 births with a population of about 1.3 million people. Use this data to answer the following questions.

a) On average, how many people were born each day of the year in Utah?

b) On average, how many people were born each day of the year in Maine?

c) What was the birth rate in Utah in births per 100,000 residents?

d) What was the birth rate in Maine in births per 100,000 residents?

It has been suggusted that the highest priority of retirees is travel. Thus, a study was conducted to investigate the differences in the length of stay of a trip for pre- and post-retirees. A sample of 683 travelers were asked how long they stayed on a typical trip. The observed results of the study are found below.

With this information, construct a table of estimated expected values.

Now, with that information, determine whether the length of stay is independent of retirement using α=0.05α=0.05.

(a) χ2=χ2=

(b) Find the degrees of freedom:

(c) Find the critical value:

(d) The final conclusion is

A. There is not sufficient evidence to reject the null hypothesis that the length of stay is independent of retirement.
B. We can reject the null hypothesis that the length of stay is independent of retirement and accept the alternative hypothesis that the two are dependent.

It has been suggested that the highest priority of retirees is travel. Thus, a study was conducted to investigate the differences in the length of stay of a trip for pre- and post-retirees. A sample of 696 travelers were asked how long they stayed on a typical trip. The observed results of the study are found below.  

With this information, construct a table of estimated expected values.

Now, with that information, determine whether the length of stay is independent of retirement using alpha = 0.01

a) chi squared =

b) Find the degrees of freedom:

c) Find the critical value:

d) The final conclusion is

A. There is not sufficient evidence to reject the null hypothesis that the length of stay is independent of retirement.

B. We can reject the null hypothesis that the length of stay is independent of retirement and accept the alternative hypothesis that the two are dependent.