Acme Plumbing Supply has just received a shipment of 5,000 valves for chemical plants, where regular steel valves would corrode. However, it is known that in the shipment 50 of the valves are regular steel which were inadvertently included. Unfortunately there was no was to distinguish between the two types of valves. They
An urn contains 8 red chips, 10 green chips, and 2 white chips. A chip is drawn and replaced and then a second chip is drawn. What is the probability of? a.) A white chip on the first draw b.) A white chip on the first draw and a red on the second. c.) Two green chips being drawn. d.) A red chip on the second draw given a
1)If X and Y are both discrete, show that ʸ ̄ xPX/Y9x/y)=1 for all y such that pY(y)>0. 10) Suppose X and Y are independent continuous random variables. Show that E[X/Y=y]=E[X] for all y
52) (from pg. 52) A coin, having probabiliyt p of landing heads, is flipped until head apears for the rth time. Let N denote the number of flips required. a) Calculate E[X] for the maximum random variable fo Exercise 37. b) Calculate E[X] for X as in Exercise 33. c) Calculate E[X] for X as in Exercise 34.
30)Let X be a Poisson random variable with parameter (lambda). Show that P {X=i} increases monotonically and then decreases monotonically as i increases, reaching its maximum when i is the largest integer not exceeding (lambda). Hint: Consider P{X=i}/P{X=i-1}. 37) Let X1, X2, ...., Xn be independent random variables, each
The manager of a restaurant claims that only 3% of the customers are dissatisfied with the service. If this claim is true, what is the probability that the number of dissatisfied customers, in a random sample of 25 customers will be a) 0 b) at least 1 c) between 1 and 5 inclusive d) greater than 5 e) 25
The weights of medium oranges packaged by an orchard are normally distributed with a mean of 14 ounces and a standard deviation of 2 ounces. The weights of large oranges are normally distributed with a mean of 18 ounces and a standard deviation of 3 ounces. If we select, at random, one each of the medium and large oranges, deter
The following data are the result of a historical study of the number of flaws found in a porcelain cup produced by a manufacturing firm. Use these data and the associated probabilities to compute the expected number and the standard deviation of flaws. Flaws Probability 0 0.461 1 0.285 2 0.129 3 0
A class is given a list of 20 study problems from which 10 will be part of an upcoming exam. If a given student knows how to solve 15 of the problems, find the probability that the student will be able to answer, a. All 10 questions on the exam b. Exactly 8 questions on the exam c. At least 9 questions on the exam
Merican air flight 2705 from N.Y. to San Francisco has seats for 340 passengers. An average of 7% of the people with reservations do not show up so American Air overbooks by accepting 355 reservations for the 340 seats. We can analyze this system by using a binomial distribution with N=355 and P=0.93 (the probability that a boo
Steps: 2) Find p-hat(R), the proportion of days on which it rained given that it rained the pervious day. 3) Find p-hat (NR) the proportion of days on which it rained given that it did not rain the previous day. 4) Construct confidence intervals for both p-hat(R) and P-Hat(NR) (you can chose level of confidence)
What is Binomial Expansion?
A researcher is studying IQ levels. From past experience she knows the population mean IQ for adults is 110 and the standard deviation is 15. a) If samples of 30 IQs are selected and the sample mean is calculated for each sample, what can be said about the sampling distribution of the sample means, and why? b) If she ta
The Bell telephone co. surveyed an apartment building with 500 units to find out who subscribes to their service. Turns out 70% of the units use Bell's service. Find the probability that less than 340 units are using Bell services so we are looking for: P(X<340) Z= 340-350/10.25=-0.98
A manager must select from among ten persons to fill four job openings. Four of the candidates belong to a minority group. If the four positions are filled at random by the candidates, what is the probability that no minority group member will be selected?
An instructor has a test bank consisting of 300 easy true-false questions, 200 difficult true-false questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the test bank, what is the probability that it will be: a) An easy question b) An easy multipl
A survey of workers in the U.S. found that 2.9% work more than 70 hours per week. You randomly select 10 workers in the U.S. and ask each if he or she works more than 70 hours per week. a)find the probability that at most three people say they work more that 70 hours per week b)find the probability that at least three peopl s
Brake Pads- A brake pad manufacturer claims its brake pads will last for 38,000 miles. You work for a consumer protection agency and you are testing this manufacturer's brake pads. Assume the life spans of the brake pads are normally distributed. You randomly select 50 brake pads. In your tests, the mean life of the brake pads i
A) A coin is tossed 20 times. Find probability of getting at least 14 heads. B) A die is tossed 20 times. Find probability of getting a "1" two times. C) Three dice are tossed. Find probability that a four shows on exactly two of the dice.
35% of products made by company Z are defective. A sample of 9 products is chosen. Find: a) The probability that 2 are defective b) The probability that 3 are defective c) The probability that none are defective
A wheel with the following probabilities is spun: Prob(1)= 0.50, Prob (2) = 0.20, Prob (3) = 0.30 If the wheel is spun 3 times find probability that the sum of numbers you get = 6
The probability I'll jog today is 0.90 and the probability you'll jog tonight is 0.30. Find the probability: a) I'll jog and you don't jog. b) You'll jog and I don't jog. c) We'll both jog. d) Neither of us will jog.
A new component for an airplane is being manufactured. Each has a 70% probability of working properly. A sample of 8 components is sampled. Find probability that: A) all work properly. B) 6 work properly. C) at most 3 work properly. D) at least 1 works properly.
You buy 4 new tires. Each tire has a 0.9 probability of having a life of at least 60,000 miles. a) Find the probability you WILL NOT have to buy a new tire BEFORE you drive 60,000 miles. b) Find the probability you WILL have to replace all 4 tires BEFORE you drive 60,000 miles. c) Find the probability you will have
Colgate-Palmolive Makes a "Total" Effort In the mid-1990s, Colgate-Palmolive had developed a new toothpaste for the U.S. market, Colgate Total, with an antibacterial ingredient that was already being successfully sold overseas. However, the word antibacterial was not allowed for such products by the Food and Drug Administrat
A certain company relies heavily on phone orders. Suppose past records show that R% of all incoming phone calls to this company are orders from customers. At least how big must R be for you to be at least 90% sure that the first phone order of the day will occur on or before the tenth incoming call of the day?
Suppose a sequence of independent trials is performed where each trial results in either success or failure. Suppose X=the number of failures before the first success, with p=probability of success on any one trial. (a) Find the expected value of X. Be sure to show in detail how you got your answer. (b) Carefully interpret
A bowl contains R red and W white chips. Suppose N chips are drawn without replacement from the bowl. (a) what is the expected number of red chips among the N drawn? The expected number of white chips? (b) Justify your answers from part(a)
A fair die is rolled until win or loss occurs: For k=1 to 5: if a 6 occurs on the kth roll you win N dollars and game ends; if a number<k occurs you lose $10 and the game ends; otherwise you roll again. For k>5: if a 6 occurs on the kth roll you win N dollars and the game ends; if a number<5 occurs you lose $10 and the gam
1. The camera department of a large department store sells three different brands of cameras: Proxima, Yakima, and Tetron. Approximately 60% of the cameras sold are Yakimas with Tetrons accounting for 30% of sales and Proxima the remaining 10%. Store records show that approximately ¼ of those who purchase a Yakima return wit