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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

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 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

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

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

3 days to process a ton of sugar cane

The time required to process a ton of sugar cane in a plant in Central America in a recent year was normally distributed with a mean 2.5 days and a standard deviation of 0.5 days (i.e., 12 hours). What is the probability that it will take more that 3 days to process a ton of sugar cane? A shipment of 40 television sets contai

Probability of a randomly selected hour of calls

A car towing company averages 3 calls per hour. What is the probability that in a randomly selected hour the number of calls is 2? The random variable X represents the annual salaries in dollars of a group of teachers. Find the expected value E(X). X = {$30,000; $40,000; $50,000}. P(30,000) = .5; P(40,000) = .3; P(50,0

Calculation of probability and standard deviation

The results of a calculus exam are normally distributed with a mean of 76 and a standard deviation of 6. Find the percentage of students that scored above 70. 15.9 50.0 84.1 23.1 Find the standard deviation of the given probability distribution. x P(x) 0 0.24 1 0.01 2 0.12 3 0.1

Decision Making: Decision Trees

Suppose that one of our colleagues has $2000 available to invest. Assume that all of this money must be placed in one of three investments: a particular money market fund, a stock, or gold. Each dollar your colleague invests in the money market fund earns a virtually guaranteed 12% annual return. Each dollar he invests in the st

Probability calculations for Discrete distributions

Use the binomial probability formula to determine the probability of x successes in n trials: n=12, x=5, p=0.25 0.103 0.082 0.091 0.027 The probability is 0.7 that a person shopping at a certain store will spend less than $20. For groups of size 22, find the mean number who spend

Finding a probability based on a binomial distribution

1. Based on information, 10% of us are left-handed. If a group of 50 people are randomly selected, the mean number of left handed people in such groups is 10. Is this correct? 2. In problem #1, if 3 people are randomly selected, the probability that they are all left handed is what? 3. In problem #1 it would be unusual to

Probability Questions: 4 questions about probabilities

1. The board of directors for the ABC investment Fund has 10 members. If 3 members of randomly selected to oversee the auditors, the probability that the 3 wealthiest members are selected is 1/120. Is this correct??? 2. In problem #1, if members are elected to the positions of chairperson, vice chairperson, and treasurer how

Mean, Level Of Measurement & Probability

1. Each year, the US Energy Department publishes an Annual Energy Review that includes the per capita consumption for each of the 50 states. If the mean of these 50 values is calculated, what is the result? Is the answer the mean per capita energy consumption for the population in all 50 states combined??? 2. A set of data i

Expectation E(X) and Variance Var (X) of X

Let X be a random variable with the following probability distribution. Value of x of X P(X=x) 0 0.15 10 0.20 20 0.50 30 0.05 40 0.10 Find the expectation E(X) and variance Var (X) of X E (x) = Var (X)= Please explain.

Binomial Distribution: Genetic Trait Linked to Industrial Toxins

A wildlife biologist wants to do a test to see if there is a genetic trait linked to industrial toxins. Previous research says the trait is usually found in one out of every thirty frogs. If there are industrial toxins present in at the test site he would expect to see more frogs with the trait then exists in the general populat