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# Probability

### Probability of Sample proportion

A producer of a juice drink advertises that it contains 10% real fruit juices. A sample of 75 bottles of the drink is analyzed and the percent of real fruit juices is found to be 6.5%. If the true proportion is actually 0.10, what is the probability that the sample percent will be 6.5% or less? a.0.7211 b.0.1562 c.0.5488

### Infinite Population with a Mean

Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, exceeds 78 is a.0.4332 b.0.0668 c.0.0987 d.0.9013

### Probability and Odds in Favor of an Event

The odds in favor of an event are the number of successes divided by the number of failures. The probability of this event occurring is the number of successes divided by the sum of the number of successes and the number of failures. The number of successes is five and the number of failures is four. Find the odds in favor

### Calculate each probability for smoking by race for males

Refer to the contingency table shown below. (a) Calculate each probability (i-vi) and explain in words what it means. (b) Do you see evidence that smoking and race are not independent? Explain. (c) Do the smoking rates shown here correspond to your experience? (d) Why might public health officials be interested in this type o

### Probability and Binomial Distribution

6. The industry standards suggest that 10% of new vehicles require warranty service within the first year. A dealer sold 15 Nissans yesterday. Use equation (page 209) for part a) and Table II in back of book for part b) & c). Explain how you got values from table. a) What is the probability that none of these vehicles requi

### Conditional Probability and Joint Probability

2. For the following table, what is the value of : a) P(A1) b) P(B1&#9474;A2) c) P(B2 and A3). Compute this as P(B2)*P(A3&#9474; B2) . In what row and column will you find this answer? Rows are B1 & B2: columns are A1, A2 & A3. Second Event First Event A1 A2 A3 Total B1 2 1 3 6 B2 1 2 1 4

### Normal distribution: probability of observing an event.

2. The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a std dev of 2 ounces. What percentage of items will weigh at least 11.7 ounces? "?" =

### Exponential distribution for sequence of independent

The solution addresses the following questions: If X1 , X2, X3.....Xn , a sequence of independent , identically distributed( iid) random variables with finite mean µ and finite( non zero) variance σ2 then the distribution of.....

### Binomial Distribution Explained in the Solution

The solution addresses (see attachment): Determine the cumulative distribution function of a binomial random variable with n =3 nad p = ½ Determine the cumulative distribution function of a binomial random variable with n =3 nad p = 1/4 n = 10 and p = 0.01.

### Excel to Solve Probabilities -Distributions -Degrees of Freedom

I'm having a problem Using Excel to Solve Probabilities - Distributions - Degrees of Freedom. The question is listed below and the question with any relevant data is attached as an excel spread sheet. PROBLEM: Determine the following quantities using Excel: (a) Find the value of x such that P (t10x ? X) = 0.75, whe

### Using Excel Functions to solve probability problems

Please help with the following problems. Provide the solution in an Excel spreadsheet. FACTS: The amount of time spent by North American adults watching television per day is normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours. PROBLEM: (a) What is the probability that a randomly selec

### Find the largest number of room reservations that this hotel can book and still be at least 95% sure that everyone who shows up at the hotel will have a room on a given night. Using 322 reservations, find the probability that at least 90% of the available rooms will be occupied on a given night. Using 322 reservations, find the probability that at least 85% of the available rooms will be occupied on a given night.

Suppose that a popular hotel for vacationers in Orlando, Florida, has a total of 300 identical rooms. Like many major airline companies, this hotel has adopted an overbooking policy in an effort to maximize the usage of its available lodging capacity. Assume that each potential hotel customer holding a room reservation, indepe

### Using Excel to Solve Probability Problems [Problem 6.25 ]

I need help in using excel to solve the following problem: Problem 6.25 FACTS: Suppose that the number of ounces of soda put into a Pepsi can is normally distributed with &#1506; =12.05 ounces and &#8706; = 0.03 ounce. [Note: &#1506; = mean and &#8706; = standard deviation] PROBLEM: USE MS EXCEL TO SOLVE

### The speed with which utility companies can resolve problems is very important.

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports they can resolve customer problems the same day they are reported in 70 percent of the cases. Suppose the 15 cases reported today are representative of all complaints. a. How many of the problems would

### Probability and Deviation

X has binomial distribution with parameters n = 20 and p = 0.1. Find the probability that X deviates from its mean by *less than or equal to* "k" multiples of its standard deviation for (a) k = 1, (b) k = 2.

### Probability of inflammation of the gums

Bad gums may mean a bad heart. Researchers discovered that 85% of people who had suffered a heart attack during a given calendar year also had periodontal disease, an inflammation of the gums. Only 29% of people who had not suffered a heart attack had periodontal disease, and only 1% of the population suffers a heart attack duri

### Binomial distribution and conditional probability

2. A process follows the binomial distribution with n = 8 and p = .3. Find P(x > 6) to 4 decimal places -- x. x x x x 3. It is estimated that 3% of the athletes competing in a large tournament are users of an illegal drug to enhance performance. The test for this drug is 90% accurate. What is the probability that an athlete w

### Discrete random variables and their probability distributions

Thirty per cent of patients undergoing particular diagnostic procedure require a sedative. In a random sample of ten patients undergoing this procedure, what is the probability that 1. At least half will require a sedative? 2. Fewer than 3 will require a sedative? 3. At least 9 will not require a sedative?

### A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of 0.5 ounces. What is the probability that a loaf is larger than 21 ounces?

A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of 0.5 ounces. What is the probability that a loaf is larger than 21 ounces?

### Statistic - A new county hospital is attempting to determine whether ...

A new county hospital is attempting to determine whether it needs to add a particular specialist to its staff. Five percent of the general hospital population in the county contracts the illness the specialist would treat. If 12 patients check into the hospital in a day, what is the probability that 4 or more will have the ill

### Probability, Samples, Confidence Intervals

5.6 A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail. (c) One or the other will fail. Show your steps carefully. 5.7The probability is 1 in 4,000,00

### Determining probability of an event & creating a ranking system

Based on the attached Excel sheet determine: 1. The probability of cases being appealed and reversed in the three different courts. 2. Rank the judges with each court. State the criteria you used and provide a rationale for your choice.

### Binomial distribution and probability of observing an event.

Jared bets on the number 7 for each of 100 spins of a roulette wheel. Because P(7) = 1/38 he expects to win two or three times. What is the probability that Jared will actually win two or more times? This was a quiz question I answered incorrectly, I want to understand how to get it if a similar question is on the mid term.

### Poisson distribution and probability

The owner of a small computer store personally sells one computer per week on the average. Use the Poisson distribution to find the probability of randomly selecting a week in which she personally sold three computers. To use excel I know I need to find the mean and x. I also know the corrct answer is .06. However, I am a

### Foundations of Probability and Statistics: mean, median, mode, standard deviation, expectation, Etc....

Please see below. Can you write out the formula and how its done, I want to learn how these are done. Please take your time, in the past I have gone back over the work and I found that it was wrong. There is also an attachment so you can see it better, I would just go off the attachment instead, I just put it on here so people

### Variance of the Distribution

Audience members at a magic show are asked to guess the suits of 20 successive playing cards drawn from a well-shuffled deck. What is the variance of the distribution of correct answers from the audience?

### Poisson distribution for a meteor falling

Say that a meteor falls somewhere in the Gobi Desert once a year on the average. Use the Poisson distribution to find the probability of randomly selecting a year in which no meteor falls in the Gobi Desert. I know the answer is .37 but do not know how to get it. Also, I do not have a scientific calculator I am using excel.

### Probability of Coin Tosses using Probability Mass Function

Consider a sequence of independent tosses of a coin. A head (H) or tail (T) is the result of the toss of a coin. P(H) = P(T) = .50. X is the random variable Let X be the number of tosses needed to get the first tail. The p.m.f., probability mass function is given by P(X=x) = (1/2)^x, x = 1,2,..., Calculate the probabilit

### Waiting Line Model

Determine the Waiting Line Model and Solve Below. 6. The Bijou Theater in Hermosa Beach, California, shows vintage movies. Customers arrive at the theater line at the rate of 100 per hour. The ticket seller averages 30 seconds per customer, which includes placing validation stamps on customers parking lot receipts and punch

### Continuous Uniform Distribution of Lengths of Statistic Classes

Please see the attached file. The diagram represents a continuous uniform distribution of lengths of statistic classes. I need to find the probability of a class of length less than 48.5 minutes. Can you please show how we arrive at that answer?