Question

Concept 8. When calculating a 95% confidence interval for a population mean, which is the most important situation where use of the t distribution would be better than use of the normal distribution? Write the letter for the best choice. A. When the sample size is small. B. when the population standard deviation is unknown. C. when the sample standard deviation is unknown. D. When the population standard deviation is known. E. When the sample size is large. For 9 and 10: Suppose we were comparing the mean age of buyers of new domestic cars to the mean age of buyers of new imported cars. Concept 9. What is the variable under consideration? A. age of buyers B. buyers of imported cars C. buyers of domestic cars D. None of the above Concept 10. What are the two populations under consideration A. age of buyers of new domestic cars and age of buyers of new imported cars B. cars and buyers C. buyers of new domestic cars and buyers of new imported cars D. None of the above Part II Problems (150 points) Show your analysis. Do not just put down a numerie answer. (a) Let A and B be two events. Suppose that the probability that neither event occurs is 3/8 What is the probability that at least one of the events occurs? (b)Let C and D be two events Suppose P(C)-0.s, PICO D) -02 and PI(CUD-0.4. What is P(D)? 2. An un contains 6 red marbles and 4 black marbles. Two marbles are drawn without replacement from the urn. What is the probability that both of the marbles are black? (a) What is the probability that the first marble is red given that the second one is black? (b) 3. An advertisement for a cold relief claims an 80% success rate. Eight patients selected at random from a large population of patients are given this cold relief. Assume that the claimed success rate is correct. Find the probability that this treatment will be successful for seven or more of these eight patients 4. A fair die is rolled and a fair coin is tossed. Find the probability that the die shows an odd number and the coin shows a head. The histogram below gives the length of service of members of the Department of English at a particular university. The classes, in years of service, are 0-4.9, 5-9.9, ete. and the vertical axis represents the number of faculty. What percent of the faculty have less than 10 years of service? 5. English 6. Data was taken on height and weight from the entire population of 700 mountain gorillas living in the Democratic Republic of Congo: htiwt | light average hcavy ll 85 190 155 7 A consulting firm employed a few consultants, who made between $300 and $1050 per weck short 170 70 Find: (a) P(a gorilla is light) (b) a gorilla has average weight given that it is tal) The Table below lists typical weekly carnings of employees. Show the Box Plot of the following data set: 300 300 300 940 300 300 400 300 400 450 800 4501050 For the tree diagram below, find the following probabilities 8. (b) P(BnD) (c) P(C) (a) P(CIA)

Answer 1

1)      
a)      
P(at least one event) = 1 - P(neither event) = 1 - 3/8=5/8      
      
b)      
P(C u D) = 1 - P(C u D)' = 1 - 0.4=0.6      
P(D) = P(C u D) - P( C ) + P(C n D) = 0.6-0.5+0.2 = 0.3      
      
      
2)      
a)      
P(both marbles black)=4/10*3/9=2/15      
      
b)      
P(first red|second is black) = 6/10*4/9=4/15