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# Probability

### Test

True/False Indicate whether the sentence or statement is true or false. Question 1 Management science involves the philosophy of approaching a problem in a subjective manner. Question 2 Once management scientist makes his or her decision and recommendation to management, then typically, his or her involvement with the

### Hiring of Workers Probability

Estimation of workers to be hired during 3 month period: # to be hired Probability ___________ _________ 0 5% 1 10% 2 15% 3 20% 4 3

### Probability Distribution of Mean Income

Mean income of a sample of workers is \$32,000 for 9 months with a standard deviation of \$3,000. Without making as assumption about probability distribution, what is the statistically expected proportion of workers that earn less than \$26,000 or more than \$38,000?

### Statistics - Mutually Exclusive

GIVEN: The probability of event A happening is 40%. The probability of event B happening is 50%. The probability of both happening is 30%. QUESTION: If A and B are mutually exclusive, what would be the probability of the union of these two events?

### Sampling and Sampling Distributions: Example Problem

A market research firm conducts telephone surveys with a 40% historical response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 150/400 = .375?

### Calculating Probability

Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server positions, the owner would like to include information on the amount of tip a server can expect to earn per check (or bill). A study of 500 recent checks indicated the server earned the following tip. Amount of

### Normal Distribution for Inexpensive Thermormeters

Assume the readings of inexpensive thermometers for the temperature of the freezing point of water are normally distributed, have a mean of 0 degree C, and a standard deviation of 1 degree C. Find the probability that a randomly selected thermometer will have a reading of greater than -2 degree C for the freezing point of water.

### Computing Probabilities: Example Problems

For a normally distributed population, mean of 6.5 and standard deviation of 4, compute: The probability of picking one item from the population and having it fall between 6.5 and 14.5. The probability of picking one item and have it be above 14.34. The point if the probability of picking an item from the population and h

### Raining Probabilities of Miami and Phoenix

According to the National Climatic Data Center, Miami, Florida experienced 138 days of measurable precipitation (rain) in 1995. By comparison, the weather station at Phoenix, Arizona reported 31 days of precipitation during the same year. Neither amount of precipitation was considered unusual for these two cities. a. A day i

### Susan Williams has been the production manager of Medical Suppliers, Inc.

Susan Williams has been the production manager of Medical Suppliers, Inc., for the past 17 years. Medical Suppliers, Inc., is a producer of bandages and arm slings. During the past 5 years, the demand for No-Stick bandages has been fairly constant. On the average, sales have been about 87,000 packages of No-Stick. Susan has

### Decision Tree and Probability

Problem: Bill Holiday is not sure what he should do. He can either build a quadplex (i.e., a building with four apartments), build a duplex, gather additional information, or simply do nothing. If he gathers additional information, the results could be either favorable or unfavorable, but it would cost him \$3,000 to gather th

### Finding a probability based on a table

Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category. Male (M) Female (F) Job Administrative (AD) 110 20 Salaried staff (SS) 30

### Compute a probability: Example problem

Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 55% for University Y. What is the probability that Jim will be accepted at both universities?

### Joint Probability

A joint probability can have a value ________ one. greater than less than equal to A and C B and C

### Finding a probability based on a binomial distribution

You have two kids. A door to door salesman knocks on your door. Your little girl answers. Assume that the chance of having a girl/boy baby is 50% and is independent. What is the probabllity that the second child who is still watching TV is also a girl?

### Probability: binomial experiment

Consider a binomial experiment with 2 trails and p= 0.4. find the probability of at least one success.

### Probability of a Call

Telephone calls arrive at the rate of 48 per hour at the reservation desk for the Paris Hilton. Find the probability of receiving 3 calls in five minute period.

### Hypergeometric Question on Training Enrollment

I can do the Hyper formula f(x) = r N-r x n-x divided by N n but I cant figure out all my needed numbers from the problem. Problem states 20% enrolled in training dropped out without co

### Probability - Nationality

We would like to make a study of poverty between Americans and Canadians. Company x picked a total of 1,000 American and Canadians in a survey. Upon examination of the collected data, it is found that there are 643 Canadians and 357 Americans in the survey. And 403 of the Canadians are rich and 240 are poor. Of the Americans

### Probability with and without replacement

Company x manufactures toy panzers. Suppose that in an assortment of 20 toy panzers, there are 5 with defective turrets. Draw with and without replacement. a. If one panzer is selected at random, what is the probability that it has defective turret? b. If two panzers are selected at random, what is the probability tha

### Probability in Statistics

The sales records of a real estate agency show the following sales over the past 200 days: Number of Number Houses Sold of Days 0 60 1 80 2 40 3 16 4 4 a. How many sample points are th

### Alpha Difference

Why do alphas differ among industries?

### Probability of Lottery Winnings

What is the probability you will win any money in the state lottery and the probability that you will win at least \$100, if the payoff for \$2.00 is 0.0200; \$25.00 is 0.0100; \$100 is 0.0050; \$500 is 0.0010; \$5000 si 0.0005 and \$10,000 is 0.0001? Please show step by step in detail of how you compute the answers.

### Important information about Intersection and conditional probability

Suppose that a certain college class contains 45 students. Of these, 26 are sophomores, 25 are chemistry majors, and 7 are neither. A student is selected at random from the class. (a) What is the probability that the student is both a sophomore and a chemistry major? (b) Given that the student selected is a chemistry ma

### Calculate the best expected pay off (EMV).

Suppose a product needs to be marketed, but the manufacturer can make the product in three ways using any one of the three designs. There are three categories of market conditions and they occur with the probabilities given in the following table: Design Market condition I with probab

### Probability, Mean

1. A manufacturer of batteries for "kids' toys" wishes to investigate the length of time a battery will last. Tests results on a sample of 10 batteries indicated a sample mean of 5.67 and a sample standard deviation of 0.57. a. Determine the mean and the standard deviation b. What is the population mean? What is the best e

### Normal distribution raw scores

Suppose that scores on a particular test are normally distributed with a mean of 130 and a standard deviation of 19. What is the minimum score needed to be in the top 5% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place. Can y

### Probability Machine

A machine is set to pump cleanser into a process at the rate of 7 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 6.5 to 7.5 gallons per minute. Find the probability that the machine pumps less than 6.75 gallons during

### Find the Probability - Sample Mean Weight

The amount of corn chips dispensed into a 10 ounce bag by the dispensing machine has been identified at possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of .2 ounces. Suppose 100 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weig

### Tree Diagram & Probability

A course in statistics is one of the most difficult at the local university. Because of this, for the past decade the university has arranged for teaching assistants to hold frequent discussion sessions as part of the course. Since the inception of the discussion sessions, 50% of the students enrolled in the course regularly att