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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 Colored Marbles

A container has 6 blue marbles, 2 red marbles, and 3 green marbles. if 3 marbles are drawn without replacement, what is the probability that all three will be blue?

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

Sampling, Central Limit Theorem and Confidence Intervals Discussion Questions

Exercise 1 From Chapter 7 of Lind, submit your responses to problem #16 on pp. 237 The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the pro

Probability, mean & variance

Please help with the following probability problems. Provide step by step calculations for each statistics question. The probability that a pumpkin seed will germinate is 70%. A gardener plants in batches of 12. a. What is the probability that exactly 10 seeds will germinate? b. What is the probability that 10 or mo

Random Variables

1. Seventy percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 60% have an emergency locator, whereas 90% of the aircraft that are not discovered do not have an emergency locator. Suppose a light aircraft has disappeared. a) Draw


The p.d.f. of X is f(x)= c*x (0<X<1) a) Find c b) Find and Graph the CDF of X c) Compute E(X)

Ford Super Duty F-750

Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation 2,000 miles. a. What percent of the Ford

Binomial Probabilities

3.6-14. A candy maker produces mints that have a label weight of 20.4 grams. Assume that the distribution of the weights of these mints is N(21.37, 0.16). a) Let X denote the weight of a single mint selected at random from the production line. Find P(X > 22.07). b) Suppose that 15 mints are selected independently and weighed.

True Statement

Fred's Surfboard Shop makes surfboards by hand. The number of surfboards that Fred makes during a week depends on the wave conditions. Fred has estimated the following probabilities for surfboard production for the next week. Number of Surfboards 5 6 7 8 9 10 Probability 0.13 0.22 0.3 0.1 0.15 0.1 Let event A be that Fred pro


Three friends toss one coin each to determine a winner. The person whose coin shows up different from the other two coins wins. What is the probability that there is no winner? a. 0 b. 1/8 c. 1/4 d. 1/2


A certain medical test has the following characteristics. In case of a viral infection, the test shows positive with probability 0.8. Even if there is no viral infection, the test shows positive with probability 0.1. There is a 1/5 chance that any patient has a viral infection. If a patient tests positive on this test, what is t

Electric Razor Case Study: Using a Decision Tree to Solve a Problem

[See attachment for case study] a) Draw a decision tree to solve Jim's problem. Explain how you have calculated all the probabilities that you report on the tree. Define clearly each decision node, event node, decision that you can take, and possible outcome for the random variables. b) What is the best decision for Jim am

Probability problems

18 owned tents, 15 owned sleeping bags, 14 owned camping stoves, 6 owned both tents and camping stoves, and 10 owned both sleeping bags and camping stoves: a. What is the probability of owning a tent, owning a camping stove, owning a sleeping bag, camping stove, and owning both a sleeping bag and a camping stove? b. What is

Continuous distribution

1. Let the random variable X have the p.d.f. f(x)=2(1-x) for 0<x<1 and zero elsewhere. a. Sketch the graph b. Determine and sketch the graph of the distribution function of X c. find P(X) for the following intervals: i. [0,1/2] ii. [1/4,3/4] iii. X=3/4 iv. X>3/4 2. For each of the following functi