Ap Statistics Quiz 8: Conditional Probability, Means And Variances Of Random Variables

AP STATISTICS | FIESTA 8 | FALL 2008 | SHUBLEKA    

Conditional Probability & Rules for Means and Variances of Random Variables NAME__________________________ Use full English sentences and write your answers on a separate page. Show all your work for full credit. Problem 1 The probability that a randomly chosen student at the University of New Harmony is a woman is 0.6. The probability that the student is studying educations is 0.15. The conditional probability that a student is a woman, given that the student is studying education, is 0.8. What is the probability that the student is studying education, given that she is a woman? Problem 2 The amount of nitrogen oxides NOX present in the exhaust of a particular type of car varies from car to car according to the Normal distribution with mean 1.4 grams per mile and standard deviation 0.3 grams/mile. Two cars of this type are tested. One has 1.1 g/mi of NOX; the other has 1.9. The test station attendant find this much variation between two similar cars surprising. If X and Y are independent NOX levels for cars of this type, find the probability: P ( X − Y ≥ 0.8 or

X − Y ≤ −0.8 ) that the difference is at least as large as

the value the attendant observed. Problem 3 Rotter Partners is planning a major investment. The amount of profit X is uncertain, but a probabilistic estimate gives the following distribution (in millions of dollars): Profit: Probability:

1 0.1

1.5 0.2

2 0.4

4 0.2

10 0.1

a) Find the mean profit and the standard deviation of profit b) Rotter Partners owes its source of capital a fee of $200,000 plus 10% of the profits X. So the firm actually retains Y = 0.9X – 0.2 from the investment. Find the mean and standard deviation of Y.