Problem 2 Consider the following (x,y) values: 0 2 4 3 5 4 Answer the following

Question

Problem 2

Consider the following (x,y) values:

0 2

4 3

5 4

Answer the following questions.

a. Plot the scatter diagram, not using Excel.
b. Calculate the means and medians of x and y, respectively.
c. Calculate the sample variances and standard deviations of x and y, respectively. Compare their variances, and comment.
d. Calculate the sample covariance of x and y. Comment.

Problem 3

Morningstar tracks the total return for a large number of mutual funds. The following tale shows the total return and the relative frequency for four categories of mutual funds.

Type of Fund Relative Frequency Total Return

Domestic Equity 57% 4.65

International Equity 16% 18.15

Specialty Stock 9% 11.36

Hybrid 18% 6.75
Total 100%

Using the relative frequencies as weights, compute the weighted average total return for the mutual funds covered by Morningstar.

Problem 4

A large consumer goods company ran a television advertisement for one of its soap productions. On the basis of a survey that was conducted, probabilities were assigned to the following events.

B = individual purchased the product
S = individual recalls seeing the product

B S = individual purchased the product and recalls seeing the advertisement

The probabilities assigned were P (B) = 0.20, P (S) = 0.40, P (B S) = 0.12.
a. Make a Venn diagram.
b. What is the probability that an individual purchased or recalls seeing the advertisement.
c. What is the probability of an individual purchasing the product given that the individual recalls seeing the advertisement?
d. Based on your answer in c, does seeing the advertisement increase the probability hat the individual will purchase the product?

Problem 5

In Rochester International Airport, 40% of the arrivals are Southwest Airlines flights,and 60% of the arrivals are US Airway flights. The U.S. Department of Transportation reported that during November, 83.4% of Southwest Airlines’ flights, and 75.1% of US Airways’ flights arrived on time in Rochester International Airport.

a. What is the probability that a flight will arrive on time and is Southwest Airlines’ flight?

Problem 6
a. How many ways to pick president, secretary and treasurer from a group of 5 people?

b. How many ways to get 3 heads, if you flip a coin 5 times (the order does not matter)?

Explanation / Answer

Please post 1 question at a time as per forum rules. Write back in case you have doubts.

6.

a. There are 5 people in total

Way to pick President, secretary and treasurer, is equal to choosing any 3 of the total 5 people

So, this can happen in 5C3 = 10 ways

b. The same goes with this part. 3 heads can come out in 5 tosses in 5C3 ways = 10 ways

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