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1- The following data is a sample of profit or loss (in million dollars) of 7 corporations

XXXXXXXXXX 35

a) Find the sample mean and variance of profits.

b) Find the range, and median of profits.

**2**- A survey was conducted at a university. 30 students randomly selected and asked if they are watching March Madness games. Their answers (Y = yes, N = no) and their gender (M = male, F = female) follows:

Watch N N N Y Y Y N Y Y N Y N N Y Y Y N N Y N N Y N N N Y N Y N N

Gender F F F M F F M M M M M F F M F M M F M M F M F F F F F M M F

a) What is the probability that a student is male and watches the games?

b) If a selected student is female, what is the probability that she watches the game?

c) Is “Watching basketball” independent of “Gender”?

**3**- A grocery store has shelf space for 60 units of a perishable item that must be disposed of at the end of the day if it is not sold. Each unit cost $2.8 and sells for $5.50. Demand probabilities are as follows: P(10 items sold) = 0.20, P(30 items sold) = 0.25, and P(60 items sold) = 0.45. Let X denote the random variable of daily profit (loss) if the grocery stocks 50 items.

a) Show the probability distribution of X.

b) What is the expected daily profit (loss) of the grocery.

**4**- The probability of an accident on any given day at a large manufacturing plant is 0.20.

a) What is the probability that on 4 consecutive days no accidents occur?

b) What is the probability that an accident occurs on at least 1 of 3 days.?

c) How many accidents you expect to occur over 100 days of operations?

**5**- A sample of 100 students taking introductory statistics courses were asked the number of hours per week they study. The results are shown in Table 1.

Table I: Frequency of Hour Study

# of Hours Frequency Relative Freq.

--------------------------------------------------------------

1 28

XXXXXXXXXX

3

6 6

More than 6 2

---------------------------------------------------------------

Complete the table. Based on the sample information if a student in statistics class

randomly selected, what is the probability that

a) the student studies 3 hours per week?

b) the student studies at least 3 hours per week?

**6**- You are presented with two investment opportunities, investment X and investment Y. The accompanying data record financial analyst's assessment of the possible gains or losses (in 1000 dollars) from each investment, and their associated probabilities.

Investment 1 Investment 2

X P(X = x_{i}) Y P(Y= y_{i})

--------------------------------------------------------------

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

a) Which investment is preferable in terms of expected return?

d) Assume you are a risk averse. If the standard deviations of X and Y are 25.9

and 37.4, respectively, which investment you prefer?

**7**- A group of 800 adults working for Wall Street firms participate in a randomize response poll. They are asked to roll a die and answer question A if the outcome is an even number, otherwise answer question B.

A: Do you work in financial market?

Y N

B: Have you ever cheated on your tax return?

There are 490 Yeses. Estimate the proportion of the Wall Street firms’ employees who cheat on their tax return.

May 12, 2021

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