4 Short Statistics Questions. Help!

Hi there are 4 short statistics questions and it would be great if i could get them in 2 days. Thanks!

Name: EC

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303 Foundations for Econometrics
Matriculation #: PS3
Tutorial Section (W#):

Week 6: Problem Set 3

DUE: Monday 30 September,

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2pm

• Please hand in to the economics office (AS2 – L6)

• Late assignments will not be accepted.

• Show your work to get full credit.

• Carry through fractions or exact decimals when possible, or round to
four decimal places. Please round final answers to four decimal places.

1. (3 pts) In a given population of two-earner male/female couples, male earnings have a
mean of $30,000 per year and a standard deviation of $1,000. Female earnings have a
mean of $35,000 per year and a standard deviation of $1,800. The correlation between
male and female earnings for a couple is 0.80. Let C denote the combined earnings for a
randomly selected couple.

(a) What is the mean of C?

(b) What is the covariance between male and female earnings?

(c) What is the standard deviation of C?

2. (3 pts) In survey taken two years ago by all employees of StatsWorld, Inc., 53% of em-
ployees were concerned about future health care benefits. This year, the company asked a
random sample of only 80 employees if they were concerned about future health care ben-
efits. Answer the following, assuming that for the entire company, the share of employees
concerned about health care benefits has not changed since the first survey.

(a) What is the standard error of the sample proportion who are concerned about future
health care benefits?

(b) What is the probability that the sample proportion concerned is less than 0.5?

(c) What is the upper limit of the sample proportion concerned, such that the sample
proportion concerned would exceed this value only 3% of the time?

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EC2303 – Foundations for Econometrics Version: September 17, 2013

3. (2 pts) A town has 500 real estate agents. The mean value of the properties sold in a year
by these agents is $800,000, and the standard deviation is $300,000. A random sample of
100 agents is selected, and the value of the properties they sold in a year is recorded.

(a) What is the standard error of the sample mean?

(b) What is the probability that the sample mean is between $790,000 and $820,000?

4. (2 pts) Let X be the amount won or lost in betting $5 on red in roulette. In the spin of a
roulette wheel (American style) there are 18 red numbers, 18 black numbers, and 2 green
numbers (0 and 00). Hence, px(5) = 1838 and px(−5) =

20
38
. Suppose a gambler bets on red

100 times.

(a) What is his expected payoff?

(b) What is the probability that the gambler walks away with less than $50 in losses?

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