Statsci Pe2 Answer Key
2
STATSCI PRACTICE EXERCISE 2 1. The availability of venture capital has provided a big boost in funds available to companies in recent years. According to Venture Economics, 2374 venture capital disbursements were made in 1999. Of these, 1434 were to companies in California, 390 were to companies in Massachusetts, 217 were to companies in New York, and 112 were to companies in Colorado. Twenty-two percent of the companies receiving funds were in the early stages of development, and 55% of the companies were in the expansion stage. Suppose you want to randomly choose one of these companies to learn about how they used the funds. a. What is the probability the company chosen will be from California? 1434/2374 b. What is the probability the company chosen will not be from one of the four states mentioned? 221/2374 c. What is the probability the company will not be in the early stages of development? 0.78 2. When tossing two dice, there are six possible even values (2, 4, 6, 8, 10 and 12), and only five possible odd values (3, 5, 7, 9 and 11), and hence, even values should occur more frequently then odd values. Do you agree with this statement? Explain. No, since the probabilities for each of these outcomes are different. 3. Suppose we have a sample space S = {E 1 , E 2 , E 3 , E 4 , E 5 , E 6 , E 7 }. The following probability assignments apply: P(E 1 ) = .05, P(E 2 ) = .20, P(E 3 ) = .20, P(E 4 ) = .25, P(E 5 ) = .15, P(E 6 ) = .10, P(E 7 ) = .05. Let A = {E 1 , E 4 , E 6 }, B = {E 2 , E 4 , E 7 }, and C = {E 2 , E 3 , E 5 , E 7 }. a. Find P(A), P(B), and P(C). 0.40, 0.50, 0.60 b. Find A B and P(A B). A B={E1, E2, E4, E6, E7} P(A B)=0.65 c. Find A B and P(A B). A B ={E4} P(A B)=0.25. d. Are events A and C mutually exclusive? Yes e. Find B’ and P(B’). B’={E1, E2, E5, E6} P(B’)=0.50 4. A survey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons. a. What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons? 0.698 b. What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons? 0.302 5. A sample of 200 students from three colleges were asked if they favored the four days per week schedule over the original five days per week. The results are shown below: COS CLA CED Tot al In Favor 30 15 35 80 Not In Favor 20 85 15 120 Total 50 100 50 200 Suppose a student is selected at random from this sample. What is the probability that we select a (1 point each) i. student from the COS? 50/200
-
Upload
mohamad-azizi -
Category
Documents
-
view
220 -
download
0
description
uig
Transcript of Statsci Pe2 Answer Key
STATSCI PRACTICE EXERCISE 2
1. The availability of venture capital has provided a big boost in funds available to companies in recent years. According to Venture Economics, 2374 venture capital disbursements were made in 1999. Of these, 1434 were to companies in California, 390 were to companies in Massachusetts, 217 were to companies in New York, and 112 were to companies in Colorado. Twenty-two percent of the companies receiving funds were in the early stages of development, and 55% of the companies were in the expansion stage.Suppose you want to randomly choose one of these companies to learn about how they used the funds.
a. What is the probability the company chosen will be from California? 1434/2374b. What is the probability the company chosen will not be from one of the four states mentioned? 221/2374c. What is the probability the company will not be in the early stages of development? 0.78
2. When tossing two dice, there are six possible even values (2, 4, 6, 8, 10 and 12), and only five possible odd values (3, 5, 7, 9 and 11), and hence, even values should occur more frequently then odd values. Do you agree with this statement? Explain. No, since the probabilities for each of these outcomes are different.
3. Suppose we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}. The following probability assignments apply: P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, P(E7) = .05. Let A = {E1, E4, E6}, B = {E2, E4, E7}, and C = {E2, E3, E5, E7}.
a. Find P(A), P(B), and P(C). 0.40, 0.50, 0.60b. Find A B and P(A B). A B={E1, E2, E4, E6, E7} P(A B)=0.65c. Find A B and P(A B). A B ={E4} P(A B)=0.25.d. Are events A and C mutually exclusive? Yese. Find B’ and P(B’). B’={E1, E2, E5, E6} P(B’)=0.50
4. A survey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons.
a. What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons? 0.698
b. What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons? 0.302
5. A sample of 200 students from three colleges were asked if they favored the four days per week schedule over the original five days per week. The results are shown below:
COS CLA CED TotalIn Favor 30 15 35 80
Not In Favor 20 85 15 120Total 50 100 50 200
Suppose a student is selected at random from this sample. What is the probability that we select a (1 point each)
i. student from the COS? 50/200ii. student who is not from the COS? 150/200iii. student who is in favor of the four days per week schedule? 80/200iv. student from the CLA who does not favor the four days per week schedule? 85/200
6. If the probability that Tom will be alive in 20 years is 0.7 and the probability that Nance will be alive in 20 years is 0.9, what is the probability that neither will be alive in 20 years? 0.03
7. The heights of 1000 students are normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters.
A. What is the probability that students will have a height between 171.5 and 182 centimeters? 0.5296
B. What is the probability that students will have a height greater than or equal to 188 centimeters? 0.0252
C. How many of the 1000 students will have heights less than 160 centimeters? 1788. The probability that a fluorescent light has a useful life of at least 800 hours is 0.9.
A. Find the probabilities that among 20 such lights, exactly 18 will have a useful life of at least 800 hours. (5 points) 0.2852
B. Find the probabilities that among 20 such lights, at least 2 will not have a useful life of at least 800 hours. 0.6083
9. The average number of field mice per acre in a wheat field is estimated to be 12.A. Give the standard deviation of X, where X is the number of mice per acre. 3.4641
B. Find the probability that fewer than 7 field mice are found on a given acre. 0.0458
![PE2- UPSCTREE PRELIMS TEST SERIES€¦ · UPSCTREE [PRELIMS TEST – PE2 –ECONOMY] 1 PE2- UPSCTREE PRELIMS TEST SERIES Economy Survey- Part 1, Budget- Part 1 ; Current Events Q.1)](https://static.fdocuments.in/doc/165x107/5f9ba52a2ca76b373f72e91a/pe2-upsctree-prelims-test-series-upsctree-prelims-test-a-pe2-aeconomy-1-pe2-.jpg)
