BUSINESS STATISTICS MID-TERM

Name:

Instruction: Your final answer should be clearly written in the assigned space for each question.

1. (10 points each, a total of 20 points) An investment advisor recommends the purchase of shares in Infogenics, Inc as he expects that the stock of Infogenics would go up at least 20%. He thinks that the chance of profit from the investment could depend on the GDP (Gross Domestic Products). Specifically, he made prediction for the chance of stock going up 20% given three different scenarios; when rising in GDP, the probability of stock going up 20% are 60%, the probability would be 50% with level GDP. Lastly, when fall in GDP, the probability of going up 20% would be 40%. An economist has also predicted that the probability of a rise in the GDP is 30%, whereas the probability of a fall in the GDP is 40%.

a. What is the probability that the stock will go up 20%?

b. We have been informed that the stock has gone up 20%. What is the probability of a rise or fall in the GDP?

2. (10 points each, a total of 20 points) The following probability model describes the number of snowstorms for Washington, D.C. for a given year:

Number of Snowstorms	0	1	2	3	4	5	6
Probability	.25	.33	.24	.11	.04	.02	.01

The probability of 7 or more snowstorms in a year is 0.

a. What is the probability of more than 2 but less than 5 snowstorms?

b. Given this a particularly cold year (in which 2 snowstorms have already been observed), what is the conditional probability that 4 or more snowstorms will be observed?

4. (5 points each, a total of 20 points) Twenty-five percent of the employees of a large company are minorities. A random sample of 7 employees is selected.

a.	What is the random variable (in English) and which distribution can you assume for the random variable?
b.	What is the probability that the sample contains fewer than 2 minorities?
c.	What is the expected number of minorities in the sample?
d	What is the variance of the minorities?

4. (10 points each, a total of 40 points) Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6.

a.	What is the probability that a randomly selected exam will have a score of at least 71?
b.	What percentage of exams will have scores between 89 and 92?
c.	If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?
d.	If there were 334 exams with scores of at least 89, how many students took the exam?

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