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probability and SD, mean

The amount of time a bank teller spends with each customer has a population mean mx = 3.1 minutes and population standard deviation sx = 0.4 minute. a) What is the probability that for a randomly selected customer the service time would exceed 3 minutes? b) If many samples of 64 were selected, what are mean and standard e

Probability Problems including Continous Random Variables

I have 100 items of a product in stock. The probability mass function for the product's demand D is P(D=90)=P(D=100)=P(D=110)=1/3 a) find the mass function, mean and variance of the number of items sold. b) find the mass function, mean, and variance of the amount of demand that will be unfilled because of the lack of stock.

The following table is from the Social Security Actuarial Tables.

7) The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number of living out of an original 100,000 and the additional life expectancy for a person of that age. Determine the following using the table: a. To what age may a female of age 60 expec

Find the Mean for the Binomial Probability Distribution.

Imagine you are the CEO of a local bank whose credit card holders engage in 1 billion credit card transactions per year; that the likelihood of a fraudulent transaction is 2%; that the average transaction purchase value for all transactions is equal to $38.50; and that the bank bears the full cost of all fraudulent transactions

Quantitative Method for a New Airline

Nw Airlines is studying its service from Atlanta to Chicago. Historical data shows that the mean number of passengers per flight is 110. If the number of passengers flying NW Airlines is normally distributed and with a variance of 96 passengers; a. What is the probability that a randomly selected flight will carry between 100


1) For the following questions, would the following be considered "significant" if its probability is less than or equal to 0.05? a.Is it "significant" to get a 12 when a pair of dice is rolled? b. Assume that a study of 500 randomly selected school bus routes showed that 480 arrived on time. Is it "significant" for a schoo

Probability Distribution: Cards, Cummulative Distribution

Construct the probability distribution for the value of a 2-card hand dealt from a standard deck of 52 cards (all face cards have a value of 10 and an ace has a value of 11). a. What is the probability of being dealt 21? b. What is the probability of being dealth 20? c. Construct a chart for the cumulative distribution fun

Find mean and standard deviation from probability distribution

Dogs Households 0 1327 1 402 2 162 3 47 4 28 5 11 (a) Use a frequency distribution to construct a probability distribution x P(x) 0 1 2 3 4 5 Round to the nearest Thousandth as needed Dogs 0 1 2 3 4 5 Households 1327 402 162 47 28 11 (b) Find the mean of the probability distribution U =

Probability: Problem and Solution

Based on past experience, the poise department of the city of laurel knows that 50% of the automobiles reported stolen are recovered. In a month in which 30 automobile are stolen, what is the probability that a. 13 or more of the stolen automobile will be recovered. b. Less than 22 automobiles will be recovered. c. Between

Binomial Probability: Expected Value and the Standard Deviation

In the past few years out sourcing over seas has become more frequently used than before by U.S. companies. However, out souring is not with out problems. A recent survey indicates that 20% of the companies that outsource over seas use consultant. Suppose 7 companies that outsource are selected randomly (use formula) a. What

Probability Distribution for a New Boutique

A clothing store owner opens a new boutique and is working on a 3-day forecast of sales during the grand opening of the boutique. The owner determines that there is a 40% probability that customers will visit the store and make a purchase, which means 60% will visit the store and not make a purchase. How do you determine the pro

Gambling Odds

The State of Ohio plays a daily (except Sunday) three digit lottery, where the player chooses any three numbers, 1 thru 10, three different times. In other words, the player chooses a number value between 000 and 999. If the state, to make things more interesting, ads a fourth ball to be drawn, one red out of ten balls, how does

Probability problem of daily lotteries

The State of Ohio plays a daily (except Sunday) three digit lottery, where the player chooses any three numbers, 1 through 10, three different times. In other words, the player chooses a number value between 000 and 999. If the state, to make things more interesting, ads a fourth ball to be drawn, one red out of ten balls, how d

Opportunity-loss table

The following is an opportunity-loss table. The probabilities for the states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a person were to use the expected opportunity loss criterion, what decision would be made? A. Alternative 1 B. Alternative 2 C. Alternative 3 D. State of Nature C E. State

Discrete Probability Variable Questions

What are examples of variables that follow a binomial probability distribution? What are examples of variables that follow a Poisson distribution? When might you use a geometric probability?


Performance/Sector BioTech IT Positive 23% 17% Negative 7% 53% The table above displays data on the composition and performance of the Massachuse

Using a theorem to solve a probability problem

Please see attachment for the full question. A random sample of size n is drawn without replacement from an urn containing r red chips and w white chips. Define the random variable X to be the number of red chips in the sample. Use the summation described in Theorem 3.5.1 (see attachment) to prove that E(X) = rn/(r + w)

Statistics random variables

Cellophane that is going to formed into bags for items such as dried beans or bird seed is passed over a light sensor to test if the alignment is correct before it passes through the heating units that seal the edges. If the alignment is too bad, the process is stopped and an operator adjusts it. These stops occur ramdomely and

Random Variables

Your company bids for two contracts. You believe the probability that you get contract #1 is 0.8. If you get contract #1, the probability that you also get contract #2 is 0.2, and if you do not get contract #1 the probability that you get contract #2 will be 0.3. a. Are the outcomes of the two contract bids independent? b. F

Random Variables and Probabilities

A marketing agency has developed three vacation packages to promote a timeshare plan at a new resort. They estimate that 20% of potential customers will choose the day plan, which does not include accommodations; 40% will choose the overnight plan, which one night at the resort; and 40% will choose the weekend plan which include

Probability of a ball drawn from an urn

An urn contains five balls numbered 1 to 5. Two balls are drawn simultaneously. (a) Let X be the larger of the two numbers drawn. Find p_x(k). (b) Let V be the sum of the two numbers drawn. Find p_v(k). Repeat the question for the case where the two balls are drawn with replacement.

Probability of a white chip

Urn I contains five red chips and four white chips; urn II contains four red and five white chips. Two chips are drawn cimultaneously from urn I and placed in urn II. Then a single chip is drawn from urn II. What is the probability that the chip drawn from urn II is white?

Probability: Keno

Please show complete solutions/explanations. Keno is a casino game in which the player has a card with the numbers 1 through 80 on it. The player selects a set of k numbers from the card, where k can range from one to fifteen. The "caller" announces twenty winning numbers, chosen at random from the eighty. The amount won depe

Probability: Light Bulbs

Two lighting systems are being proposed for an employee work area. One requires fifty bulbs, each having a probability of 0.05 of burning out within a month's time. The second has onehundred bulbs, each with a 0.02 burnout probability. Whichever system is installed will be inspected once a month for the purpose of replacing b

Probability: Doomsday Airlines

Doomsday Airlines ("Come Take the Flight of Your Life") has two dilapitated airplanes, one with two engines, and the other with four. Each plane will land safely only if at least half of its engines are working. Each engine on each aircraft operates independently and each has probability p = 0.4 of failing. Assuming you wish

Generating Geometric distributions using induction

I need assistance with the attached problem. It requires me to show that a given algorithm generates the geometric distribution. Please see the attached document for details. Show that the following algorithm is valid for generating X -- geom(p) 1. Ler i=0. 2. Generate (please see the attached file) independent of any

Probability for Apartment Building

Please complete answer/steps/explanation for the following: 2.7.11. An apartment building has eight floors. If seven people get on the elevator on the first floor, what is the probability they all want to get off on different floors? On the same floor? What assumption are you making? Does it seem reasonable? Explain.

Probability of winning $10

A fast-food chain is running a new promotion. For each purchase, a customer is given a game card that may win $10. The company claims that the probability of a person winning at least once in five tries is 0.32. What is the probability that a customer wins $10 on his or her first purchase?

Poisson Distribution and MVUE.

1. Let -- be a random sample from the Poisson distribution with pmf --. Find the MVUE of --- using the following three steps. a) Find the complete sufficient statistic Y_1 for --. b) Show that -- is an unbiased estimator of -- where I is the indicator function. c) Find the MVUE of -- by the conditional expectation e(T/Y_1).