PART I Multiple choice question (50 points)

Use the following to answer next 2 questions:The probability distribution of the number of hours the evening flight from Chicago to New York is late is found to be as follows:x P(x)1 0.22 0.33 0.14 0.25 0.16 0.1

(3 p) The expected delay in the flight is: ____________

(3 p) The standard deviation of the flight delay is: ____________

Using the following data for the next 2 questions

Let X be a normally distributed random variable with = 175, = 25; (4 p) P (X < x0) = 0.1587. What is the value of x0?

a) 150 b) 200c) – 1d) Other: ______________

(4 p) Find x1 and x2 symmetrically lying on each side of the mean with P (x1 < X < x2) = 0.905:

a) 146.242; 203.758b) 150.00; 200.00c) 133.25; 216.75d) 100.20; 250.87e) Other value: __________________

(4 p) A company wants to form a project team consisting of three persons including engineer and secretary. There are 5 engineers and 3 secretaries available. What is the probability that the team consists of two engineers and one secretary?

Answer: ___________

Using the following data for the next 2 questionsThere are 4 white balls and 8 black balls in a box. If four balls are randomly selected. (3 p) The probability that exactly 2 balls are white is:

a) 0.339b) 0.406c) 0.452

d) Other:_________________

(3 p) The average number of black balls obtained when four balls are randomly selected is: a) 2.333b) 1.333c) 2.667d) Other : ______________

(2 p) A company has a new project under way and selects five executives for a transfer from their current jobs. A report had suggested that 75% of all executives in this company would like this new job. What is the probability that at least three of these five selected like their new job?

a) 0.421b) 0.456c) 0.578d) 0.896e) Other: ______________

Use the following to answer next 3 questions:

The following table gives the numbers of claims at a large insurance company by kind and by geographical region.

East South Midwest WestHospitalization 75 128 29 52Physician’s visit 233 514 104 251Outpatient treatment 100 326 65 99

A bill is randomly chosen.

(3 p) Given that bill is for hospitalization, the probability that it is from the South is: Answer: ___________

(2 p) The probability that it is either from the West or outpatient treatment:Answer: ___________

(3 p) Given that bill is from the hospitalization, the probability that it is from the Midwest is: Answer: ___________

f)Use the following data to answer next 5 questions:

The sample data size 14 is given:

320 118 256 241 309 228 267 295 185 145 184 119 178 194

(2p) Median of the above data is:a) 228b) 185.5c) 211d) 194.5

e) None of the above

(2p) Sample variance is:

a) 3938.65b) 4509.76c) 4472.67d) 4508.06e) None of the above

(2p) The 75th percentile is:

a) 263.3b) 284.5c) 287.6d) 274.0e) Other: ________________

(2p) What is the value of percentile of data point 241 ?

a) 66.2%b) 45.7%c) 65.1d) 61.5e) None of the above

(4 p) A class of business students received the following test scores on a test: 320, 410, 440, 470, 480, 480, 490, 500, 500, 510, 510, 530, 530, 530, 540, 570, 600, 650, 720, 790. How many students in this group received a score that was greater than the 75 th percent of this group?

Answer: ___________________

(4 p) Two stocks, A and B, are known to be related. The probability that stock A will go up tomorrow is 0.20 and the probability that both stocks will go up tomorrow is 0.12. Suppose that tomorrow we wind A did go up. What is probability that stock B will go up as well?

Answer: ___________

PART II - WRITING (50 points

Question 1 (10 p)In a particular city, 20% of the people subscribe to the morning newspaper, 30% subscribe to the evening newspaper, and 10% subscribe to both.

a. Determine the probability that an individual from this city subscribes to the morning newspaper, the evening newspaper, or both.

b. For a given person who subscribes to evening newspaper, what is probability that he/she will subscribes to morning paper as well?

Question 2 (10 p)A new medicine has an 85% success rate. Five patients are treated with it. What is the probability that at least four are cured with this new medicine?

Question 3 (10 p)

When economic situation is “high”, a certain economic indicator rises with probability 0.7. When the economic situation is “low”, the economic indicator rises with the probability 0.2. The economy is “high” with the probability 0.4. Given that the economic indicator has just gone up, what is the probability that the economic situation is “high”?

Question 4 (10 p)

In a certain firm, the defective products will be checked to. Past experience shows that 25% of products are defective after checked. Twenty defective products are found after a long working day.

a. What is the probability that all the defective products can be reworked?b. What is the probability that at least 18 defective ones can be reworked?

Question 5 (10 p)

A business school claims that the average income of graduates of this school three years after graduation is $700.

a. If the claim is correct and if incomes are normally distributed with a standard deviation of $60, what is the probability that 36 randomly selected graduates have an average income of less than $675?

b. If a random sample of 36 graduates had an average weekly income of $675, what would you conclude about the validity of the claim?