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Age effects in medical care. The type of medical care a patient receives may vary with the age of the patient. A large study of women who had a breast lump investigated whether or not each woman received a mammogram and a biopsy when the lump was discovered. Here are some probabilities estimated by the study. The entries in the

General Statistics

1. The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. a. What is the probability that a randomly selected teacher earns more than $525 per week? b. What is the probability a randomly selected teacher earns less than $435 per week? 2. The i

Probability of a sample proportion

A market research firm conducts telephone surveys with a 40% historic 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

Financial advisor using Decision Tree

A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation: Investment Good Economy Fair economy Poor Economy Fund A $10

Statistics questions

1. The table below describes the smoking habits of a group of asthma sufferers. Nonsmoker Occasional Regular Heavy Total _________ Smoker Smoker Smoker_______ Men 424 39 72 36 571 Women 360 46 77 44 527_ Total 784 85 149 80 1098 a. If one of the people is randomly selected, find the probability of getti

Probabilities, z scores and distributions

1. Two hundred raffle tickets are sold. Your friend has 5 people in her family who each bought two raffle tickets. What is the probability that someone from her family will win the raffle? 2. Answer the following: a. What does it mean to say that x = 152 has a standard score of +1.5? b. What does it mean to say that a

Probability Exclusive Events

1. The events A and B are mutually exclusive. Suppose P(A) = .30 and P(B) = .20. What is the probability of either A or B occurring? What is the probability that neither A nor B will happen? 2. A study by the National Park Service revealed that 50% of vacationers going to the Rocky Mountain region visit Yellowstone Park, 4

5 Statistics Questions

1. Assume that 12 jurors are selected from a population in which 50% of the people are Mexican-Americans. The random variable X is the number of Mexican-Americans on the jury. X 0 1 2 3 4 5 6 7 8 9 10 11 12 P(x) 0.000 0.003 0.016 0.054 0.121 0.193 0.226 0.193 0.121 0.054 0.016 0.003 0.000 a. Find the probability of exac

Simple Statistics Problems (Entry Level)

4. For a population with μ=50 and σ=10. a. Find the z-score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.) X = 55 X = 60 X = 75 X = 45 X = 30 X = 35 b. Find the score (X

Random Samples

1. A Private firm reports that 8% of the 2 million small businesses who apply for loan each year receive special interest rate (usually higher than market rate) because of high riskiness associated with small business. Consider a random sample of 25 small businesses who have recently applied for the loan a. What is the probab

Queuing Theory - Single-Channel Waiting Line Model

Marty's Barber Shop has one barber. Customers have an arrival rate of 5 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: a). What is the probability that no units are in the system? b). What is the probability that one customer is receiving a haircut and no one is wait

Powerball Winning Combinations, Prizes, and Probabilities

Case Study: The Powerball 1. Review the case study on page 157 of the textbook. See other attachments 2. Recall that for a single ticket a player first selects five numbers from the numbers 1-55 and then chooses a Powerball number, which can be any number between 1 and 42. A ticket costs $1. In the drawing five white balls are

Probability of Customer Complaints

Suppose that four inspectors at a film factory are suppose to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in every 200 packages. Tom, who stamps 60% of the packages, fails to stamp the expiration date once in ever

Statistics - Probability

A candy company distributes boxes of chocolates with a mixture of creams, toffees and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toffees and cordials vary from box to box. For a randomly selected box, let X = weight of creams and Y =weights of the toffees and the pdf

Combinations and Factorials

From a group of 18 customers, 4 are to be chosen to receive a special gift. Assuming that the order in which the customers are chosen is irrelevant, how many groups of 4 customers can be chosen?

Probability - Multi Project

B6. (Expected return and risk) Procter & Gamble is considering three possible capital investment projects. The projected returns depend on the future state of the economy as given here. State of the Probability of Projected Return Economy Occurance 1 2 3 Recession 0.1 9% 3% 15% Stable 0.7 13% 10% 11% Boom


The mayor of a small town would like to know whether a local bond issue is likely to pass or not. He mails a survey to 500 randomly selected voters. How many returns must he get in order to know the proportion that will support the bond issue within an error of 5% and a confidence level of 95%? If he gets a 60% return from th

Binomial Probability Distributions

Given the following information about motor vehicles, motor vehicle accidents and cost of repair for last year: # of registered motor vehicles (millions) 215 # of vehicles involved in an accident (millions) 21.3 Cost of accident ($ billions) 192 A) What is the probability that a randomly selected vehicle is involved i

Help needed with probabilities

See attached file which includes the data, The attached excel file contains data obtained from 274 couples regarding their education level, annual salary, the value of the cars that they own, the value of their homes, their total savings value (including stocks and bonds) and their social climber index (scale of 1-10, where

Statistics of Airplanes Failing

# 5.62: A certain airplane has two independent alternators to provide electrical power. The probabilty 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 all steps carefully. a) The likelihood that the first

Probabilities in transmitting messages with noise.

When a message is sent electronically, it is usually sent as a stream of bits, each of which can be either a 0 or 1. If the digital channel is noisy, then each bit has some probability of being flipped. Assume that a message is sent through a noisy channel where the probability that any individual bit will be flipped is 0.2.

Binomial distribution

According to a recently conducted survey, 90% of all drivers in Trinidad and Tobago claim to consistently driver over the legal speed limit. Assume that this result is true for the current population of the Cayman Islands. Find the probability that, in a random sample of 20 drivers: 1. None of them drive over the legal limi

Quantitative Methods

Management Science 1. There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Find the break-even point. 2. Administrators at a university are planning to offer a summer seminar. It costs $3000 to reserve

Probabilities and statistics for a random variable

1. Let f(x) = 2e^(-(x-3)/c), 3 < x < infinity (zero otherwise) be a p.d.f. of a random variable X. a. Find c b. Find the CDF of X and sketch the CDF c. Compute P(-5 < X < 10) 2. A candy maker produces mints that have a label weight of 30 grams. Assume that the distribution of the weights of these mints is N(30, 2^2).

Probability of Defect

In a shipment of 40 television, 3 are defective. if 2 television sets are randomly selected and tested without replacement, what is the probability that both are defective?

Discrete Probability Distribution for Hand Simulations

8. Perform a hand simulation for the first three customers to arrive at a ticket booth to purchase a ticket. Discrete probability distributions for the two uncertain events are presented below in one minute intervals. Assume the ticket booth opens at 7:00 AM. Assume two digit numbers were selected from a table of random number

Probability in Recent Polls

In a recent poll, 58% of the surveyed said that they will take shorter trips to keep the vacation expenses down. If 3 people are randomly selected, what is the probility that all 3 will take shorter trips?

Probabilities of Life Insurance Purchase

In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically, one in four such customers chooses to buy life insurance from this agent. Based on the relevant binomial distribution, answer the following questions; a) What is the probability that exactly 5 customers will buy life

Weekly Demand of a Fiat Car

The weekly demand for Fiat car sales follows a normal distribution with mean 50,000 cars and standard deviation 14,000 cars. a) There is a 1% chance that Fiat will sell more than what number of cars next year? b)What is the probability that Fiat will sell between 2.4 and 2.7 million cars during the next year? Please a