SHOW ALL RELEVANT WORK TO GET CREDIT Problem 1 [12 points A random sample of 300
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SHOW ALL RELEVANT WORK TO GET CREDIT Problem 1 [12 points A random sample of 300 investors in the stock market was asked whether they invest strictly on-line, through a traditional stock broker or use both. The following crosstabulation categorizes their answers according to gender. Gender Female Male Total | Just On-Line Broker 20 50 Method of Just Traditional Broker Investing | Both Methods 150 Total 180 120 300 If an investor is randomly selected, what is the probability the investor: a. b. is male? trades just traditional line? uses just on-line broker and is female? is male or uses both methods? is female given the investor trades both methods? Are the events female and both methods independent? Explain. Problem 1 |7 points The Nationwide Motel Company has determined that 80 percent of all calls for motel reservations request non-smoking rooms. Recently, the customer service manager for the company randomly selected seven calls. Assuming that calls are independent and the probability a customer requests a non-smoking room remains constant, a. b. c. What is the probability that 3 or less calls request non-smoking rooms? What is the probability that exactly 2 calls request non-smoking rooms? What would your answer to part (b) be if 23 percent [not 80 percent of callers requested non- Smoking rooms? Problem 1 [6 points) Parts and materials for skis made by Downhill Adventures Company are supplied by three suppliers. Supplier A's materials make up 50% of what is used, Supplier B's make up 20%, and Supplier C's makes up the rest. Past records indicate that 15% of supplier A's materials are defective, 10% of B's are defective, and 20% of supplier C's are defective. It is impossible to tell which supplier the materials came from once they are in inventory. If the production manager just found some defective materials, what is the probability that it came from Supplier C? Problem 112 points) The time it takes to assemble a particular children's bicycle by a parent has been shown to be normally distributed with a mean equal to 205 minutes with a standard deviation equal to 8.5 minutes. What is the probability that a randomly selected parent will require: a. more than 220 minutes? b. between 210 and 220 minutes? c. less than 210 minutes? d. Suppose that manufacturer of this bicycle would like to advertise that **82% of parents can assemble this bicycle in XX minutes or less." What should XX be?Explanation / Answer
Problme 1)
1) P(Male) = 120/3000= 0.4
2) P(just traditional) = 80/300 =0.267
3) P(just online broker and female) =20/300 = 0.067
4) P(Male and uses both method) = 60/300 = 0.2
5) P(Female |Both methods) = P(female and both methods)/ P(both methods) = 90/150=0.6
6)P(Female) = 180/300 = 0.6
P(Both methods) = 150/300 =0.5
P(Female and both method) = 90/300 =0.3
P(Female and both method) =P(Female) * P(Both methods) = 0.6*0.5 =0.3
Hence Female and both methods are independent
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