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# Probability

### Poisson Distribution

A baseball team loses \$10,000 for each consecutive day it rains, Say X, the number of consecutive days it rains at the beginning of the season, has a Poisson distribution with mean 0.2. What is the expected loss before the opening game? An airline always overbooks if possible. A particular plane has 95 seats on a flight in wh

### Poisson Distribution

Let X have a Poisson distribution with a mean of 4. Find a) P(2<X<5) b) P(X>3) c) P(X<3) Let X have a Poisson distribution with a variance of 4. Find P(X=2) Customers arrive at a travel agency at a mean rate of 11 per hour. Assuming that the number of arrivals per hour has a Poisson distribution, give the probability th

### Judge Verdicts

1- Suppose that a judge's decision follows binomial distribution and he's incorrect verdict is 10% of the times. a) Determine the probability that in the next 10 sections he will have two incorrect verdicts. Show calculations, use table.

### Probability Assisted Strikes

Please see the attachment for fully formatted problems. 1- The assistants have .50 probability of going on strike, .40 the pilots and .15 that both go on strike. a) Determine of the probability the pilots go on strikes and if the assistant will also. Indicate the probability and that condition 2- Probabili

### Cereal Box Problem/Probability

2.5-15. One of four different prizes was randomly put into each box of a cereal. If a family decided to buy this cereal until it obtained at least one of each of the four different prizes, what is the expected number of boxes of cereal that must be purchased? Attachment contains 2 more problems.

### Probabilities and Moment Generating Function

2.5-8. Show that 63/512 is the probability that the fifth head is observed on the tenth independent flip of an unbiased coin. 2.5-9. An excellent free-throw shooter attempts several free throws until she misses. a) If p= 0.9 is her probability of making a free throw, what is the probability of having the first miss on the 13th

### Binomial distribution questions.

The questions are also found in the attached Word document, with the original formatting. In exercise 15, it supposes that a procedure produces a binomial distribution with a repeated test n times. It uses a-1 table to calculate the probability of x successes, given probability p of success in a given test. 15- n=3, x

### Normal distribution to approximate the desired probability

Merta reports that 74% of its trains are on time. A check of 60 randomly selected trains shows that 38 of them arrived on time. Find the probability that among the 60 trains 38 or fewer arrive on time. Based on the result, does it seem plausible that the on time rate of 74% could be correct?

### Percent Probability

50% probability a customer will walk through the door needing customer service. What percent of the time would you expect less than 4 customers out of twenty will require customer service? What formula would you use to get this solution?

### Probability problems

Looking for help on the following 3 questions: Births of Twins The probability that a birth will result in twins is .012. Assuming independence (perhaps not a valid assumption), what are the probabilities that out of 100 births in a hospital, there will be the following numbers of sets of twins? 48. At most 2 sets of twins

### Compose an e-mail answering gender distribution

The data set for our course is a sample of a survey conducted on the population of the American Intellectual Union (AIU). It is available via the following link: DataSet with DataSet Key which contains the following nine sections of data that will be used throughout our course: (1) Gender (2) Age (3) Department (4) Position

### Probability Distributions and Expected Value Problems

Please help answer the following problem. An insurance company sells an automobile policy with a deductible of one unit. Let X be the amount of the loss having p.m.f. .9 x=0 f(x) = { (C/x) x=1,2,3,4,5,6 (where C is a constant) Determine C and the expected value the insurance compan

### Finding Mean, Variance, PMF & Binomial Distribution: Example

1. A random variable X has a binomial distribution with mean 6 and variance 3.6. Find P(X = 4). 2. A certain type of mint has a label weight of 20.4 grams. Suppose that the probability is 0.90 that a mint weighs more than 20.7 grams. Let X equal the number of mints that weigh more than 20.7 grams in a sample of eight mints se

### Binomial dist

In a lab experiment involving inorganic syntheses of molecular precursors to organometallic ceramics, the final step of a five-step reaction involves the formation of a metal-metal bond. The probability of such a bond forming is p = 0.20. Let X equal the number of successful reactions out of n = 25 such experiments. a) Find the

### A. What is the probability that a student will finish the examination in two hours or more? b. What is the probability that a student will finish the examination in more than 100 minutes but less than 150 minutes? c. What is the probability that a student will finish the examination in more than 140 minutes?

The time needed to complete the final examination of MGSC 301 is normally distributed with a mean of 120 minutes and a standard deviation of 12 minutes. a. What is the probability that a student will finish the examination in two hours or more? b. What is the probability that a student will finish the examination in mo

### Probability

A market research firm is investigating the appeal of three package designs. The table below gives information obtained through a sample of 200 consumers. The three package designs are labeled A, B, and C. The consumers are classified according to age and package design preference. A B C Total Under 25 years 22 34 4

### Normal Probability Distribution

The E.P.A. has reported that the average fuel cost for a particular type of automobile is \$800 with a standard deviation of \$80. Fuel cost is assumed to be normally distributed. We would expect that only 10% of these cars would have an annual fuel cost greater than _______.

### Probability the machine is non-defective

A machine is made up of 3 components: an upper part, a mid part, and a lower part. The machine is then assembled. 5% of the upper parts are defective; 4% of the mid parts are defective; 1% of the lower parts are defective. What is the probability that a machine is non-defective?

### Probability of a Salespersons Potential

2. Each salesperson at Stiles-Compton is rated either below average, average, or above average with respect to sales ability. Each salesperson is also rated with respect to his or her potential for advancement - either fair, good, or excellent. These traits for the 500 salespeople were cross-classified into the following table:

### Exercises 42 & 45: Weston Materials z values; Shaver Manufacturing employee dental

Continuous Probability Distributions # 42 The accounting department at Weston Materials, Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distri

### Mean and Variance of Random Variables..

Let X equal an integer selected at random from the first m positive integer, {1, 2, ..., m}. (a) Give the values of E(X) and Var(X). (b) Find the value of m for which E(X)=Var(X). (See Zerger in the references)

### Determining Mean and Variance: Example Problems

1. Place eight chips in a bowl: Three have the number 1 on them, two have the number 2, and three have the number 3. Say each chip has a probability of 1/8 of being drawn at random. Let the random variable X equal the number on the chip that is selected, so that the space of X is S = {1, 2, 3}. Make reasonable probability assign

### Probability Calculation Using Normal Distribution and Z score

88. Refer to the Baseball 2005 data, which reports information on the 30 major league teams for the 2005 baseball season. 1. Select the variable team salary and find the mean, median, and the standard deviation. 2. Select the variable that refers to the age the stadium was built. (Hint: Subtract the year in which the stadium w

### Poisson Distribution: Probability Example Problem

In Bombay, India air pollution standards for particulate matter are exceeded an average of 5.6 days in every 3 week period. Assume that the distribution of the number of days exceeding the standards per three week period is Poisson distributed. What is the probability that the standard is not exceeded on any day during a thr

### Finding the Probability Mass Function: Example Problem

Let a chip be taken at random from a bowl that contains six white chips, three red chips, and one blue chip. Let the random variable X = 1 if the outcome is a white chip, let X = 5 if the outcome is a red chip, and let X = 10 if the outcome is a blue chip. a) Find the p.m.f. of X. b) Graph the p.m.f. as a bar graph.

### Statistics: Applying the Multiplication Rule

See attached file. Colors: Red, Yellow, Green, Blue, Red, Blue, Yellow 1. Applying the Multiplication Rule. Find the probability of randomly selecting three item and getting one that is colored red on the first selection, one that is colored green on the second selection, and an item that is colored blue on the third selec

### Compare investment success probabilities

Investment A has an expected return of \$25 million and B has an expected return if \$5 million. Market risk analysts believe the standard deviation of the return from A is \$10 million, and for B is \$30 million (negative returns are possible here). (a) If you assume returns follow a normal distribution, which investment would give

### Height and Probability

If the height of the study population is normally distributed with a mean of 69.2 inches, the standard deviation is 2.9 inches, and I choose one member of the population randomly how could I find the probability that his height is more than 67 inches?

### Statistics Problems- Variety of Problems

1. A recent issue of Fortune Magazine reported that the following companies had the lowest sales per employee among the Fortune 500 companies. Company Seagate Technology SSMC Russel Maxxam Dibrell Brothers a. How many elements are in the above data set? 5 b. How many variables are in the above data set? 2 - Sa

### Discrete Distributions

1) For each of the following, determine the constant c so that f(x) satisfies the conditions of being a p.m.f. for a random variable X, and then depict p.m.f. as a bar graph. 2) An unbiased four-sided die X has two faces numbered 0 and two faces numbered 2. An unbiased four-sided die Y has its faces numbered 0, 1, 4, and 5.