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# Probability

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### Calculating probability from a given situation using combinations.

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

### Binomial Distribution

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

### P-Hat Proportion of Rainy Days

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)

### Binomial Expansion Discussion

What is Binomial Expansion?

### Understanding and calculating probability distribution.

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

### Determining the probability using binomial distribution.

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

### Probability no minority group will be selected

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?

### Calculating the Probability from a Given Situation

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

### Normal Approximations to Binomial Distributions

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

### Probability from a Given Situation using Mean

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

### Probability

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.

### Calculating Probability of Defective Products

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

### Calculating the probability from the given situation.

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

### Independent Events..

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.

### Statistics probabilty

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.

### New Tire Probability

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

### Determining the probability from the given Colgate story.

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

### Determining the probability from the given situation.

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?

### Independent Trials

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

### Probability

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)

### Role of the Die Statistics

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

### Approximate of Cameras Sold

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

### Day Worker Probability

1. A group of day to day workers can work either 0 hours, eight hours or 12 hours at a pay rate of \$9.75 per hour. (The 12 hour day pays regular time for the first eight hours and double time for the remaining four hours.) On any given day there is a 0.2 probability of not working at all, 0.7 probability of working an eight ho

### Statistics

Question 1 Assume that you are the owner of a small business that employs two people on a telephone help desk. Records show that one of the employees is busy taking calls for 40% or the time and the other is busy taking calls 55% of the time: a) What is the probability that when a new call comes in that both of the emp

### Card Solution Probability

Please explain why in a two card hand out of a deck of 52 cards the probability of getting 2 consecutive cards is 208/1326, how did you get this?

### Joint probability distribution - marginal and conditional

Suppose that x and y have the following joint probability distribution X 2 4 _______________________________________________ 1 0.10 0.15 Y 3 0.2 0.3 5 .1 .15 Find the marginal distribution of x a

### Working with probability and combinations from a given situation.

In a shipment of 14 computer parts to Indiana State, 3 are faulty and the remaining 11 are in working order. Three elements (parts) are randomly chosen out of the shipment. What is the probability that all three faulty elements will be the ones chosen?

### Binomial probability density function

Identify each variable in the formula for the binomial probability density function. Also, explain what the fraction: n! / (n-x)!x! calculates.

### Statistics and Total Number of Matches

16 wrestlers compete in a competition. If each wrestler has one match with each of the other 15 wrestlers, what is the total number of matches.

### Sum Product using Excel

Please help with the calculations as I am new with Excel Solver, and I am having problems formulating. For the LP problems, you will need to solve using the Excel Solver. We have used the Sum Product feature when using Excel. So in cases where you can use that, please do so. See the attached file.