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Probability

Detection and Estimation

Suppose you have a coin and you want to test two hypotheses: H0: the coin is fair (that is, you get a head with probability p = 0.5 and a tail with the same) and H1: the coin is unfair and has probability p > 05 for a head and (1-p) for a tail. Assume p is known. Explain in detail what the optimum Neyman = Pearson test is fo

Weston Materials - Probability Analysis

The accounting department at Weston Materials Inc a national manufacturer of unattached garages, report 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 distribution. a. Determine the z values for 29 and 34 h

Random Selection and Probability

EBook is a digital book provider that sells their downloaded product through both Anason and Bairnes-Nolb. Anason requires that EBook use a different format than they use for Bairnes-Nolb. EBook keeps records that show the number of unacceptable downloads done by each format. Based on past data, the probability that an EBook ca

Proportion and Probability of Household Incomes

According to the U.S. Census Bureau, the mean household income in the United States in 2000 was $63,091 and the median household income was $50,054 (U.S. Census Bureau, www.census.gov, September 2011). The variability of household income is quite large, with the 85th percentile (i.e., top 15%) approximately equal to $100,000, a

Probability: Quarter Example Problems

Currently, quarters have weights that are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g. A vending machine is configured to accept only those quarters with weights between 5.550 g and 5.790 g. a) If 280 different quarters are inserted into the vending machine, what is the expected number of

Probability of Overbooking an Airplane

A Boeing 767-300 has 213 seats. When someone buys a ticket for a flight, there is a 0.0995 chance that the person will not show up for the flight (based on data from an IBM research paper by Lawrence, Hong, and Cherrier). A ticket agent accepts 236 reservations for a flight that uses a Boeing 767-300. Find the probability that

Expected Payoff - Slot Machine

A standard slot machine has three reels. The first reel has 3 walnuts, 7 cherries, 3 oranges, 5 lemons, 1 bell, and 1 jackpot bar. The second reel has 7 cherries, 6 oranges, 1 lemon, 3 bells, and 3 bars. The third reel has 4 walnuts, 7 oranges, 5 lemons, 3 bells and 1 bar. The payoffs are Reel 1 Reel 2 Reel 3 Payoff in Coi

Probability, Statistics, and Data

W1A4 Sample Questions Determine if this is an example of probability or statistics: If a red, blue, and green M&M are placed into a bag, we have a 1/3 chance of reaching in and selecting the red M&M. Determine if this data is qualitative or quantitative: Waist size Determine if this study is experimental or observational:

Normal Distribution and Values

The incomplete table at right is a discrete random variable x's probability distribution, where x is the number of courses taken by randomly selected undergraduate student. (Please refer to attached document to view the table and note that the questions are written in the excel file as well ) Answer the following: (a)

Stats Problem

Question: The table below shows the probability distribution for the daily demand of toasters at a store. DEMAND PROBABILITY 0 0.05 1 0.1 2 0.25 3 0.25 4

Analytical Estimate

a. In a class roster of 18 students, what are the chances that there are at least 2 people with the same birthday (same day, not same year)? Given a birthday of July 29th, please provide a detailed analytical estimate of the likelihood that this will happen. b. A street performer approaches you to make a bet. He shows you th

can u help please?

1. True or False? The normal distribution is the most important discrete probability distribution. 2. True or False? Every normal distribution can be transformed to a standard normal distribution. 3. For a standard normal distribution, what is the value of the standard deviation and the mean? 4. What is the area under a stan

Decision Analysis Case Study

Please see the attached case study. What is the problem facing Sam Ellis and Forward Software? (This may take 2-3 paragraphs to explain properly). Based on your decision tree, what is the course of action Sam Ellis and Forward Software should take based on the lowest EMV? (That is, what is the lowest cost alternative?) Be sur

Probability: Detecting an Income Missile

Assume that a single radar unit used to detect incoming missiles has a probability of 0.90 of correctly detecting an incoming missile attack. Furthermore, assume that four such individual and identical radar units (each with an individual probability of 0.90 of detecting an incoming missile attack) are used to create a radar ins

Analysis of Exponential Probability Distribution

The time between arrivals of customers at the drive-up window of a bank follows an exponential probability distribution with a mean of 10 minutes. a. What is the probability that the arrival time between customers will be 7 minutes or less? b. What is the probability that the arrival time between customers will be between 3 an

Uniform Distribution and Probability

The time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes. a. What is the probability that a guitar neck can be carved between 95 and 165 minutes? b. What is the probability that the guitar neck can be carved between 120 and 200 minutes? c. Determine the expected completion time for

Probability and Real World Probability

There are 2 types of probability: empirical and theoretical (classical). - Define the 2 probability types in your own words. - List 1 profession example for each probability type: empirical probability and theoretical (classical) probability. Explain clearly how these probabilities are used. - List a real-world probability

Probability of Basketball Throws

Consider a high school basketball player that is a 70% free throw shooter. During the season, what is the probability that this player makes the third free throw in five shots (exactly 3 shots in 5 attempts)?

Probability of passengers showing up

Airline overbooking is a common practice. Due to uncertain plans, many people cancel at the last minute or simply fail to show up. Air Eagle is a small commuter airline. Its past records indicate that 80% of the people who make a reservation will show up for the flight. The other 20% do not show up. Air Eagle decided to book 12

Probability of Random Draws

A box contains 10 chips. The chips are numbered 1 through 10. Otherwise, the chips are identical. From this box, we draw one chip at random, and record its value. We then put the chip back in the box. We repeat this process two more times, making three draws in total from this box. 1. How many elements are in the sample spac

Probability with a coin toss

A coin is tossed 4 times. Let "A" be the event that the first toss is heads. Let "B" be the event that the third toss is heads. 1. What is the probability that the third toss is heads, given that the first toss is heads? 2. Are "A" and "B" independent? Why or why not?

Poisson Distribution Probability Problem

During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes. [Hint: It is a Poisson Distribution Problem.] a) What is the expected number of calls per hour? b) What is the probability of three calls in five minutes? c) What is the proba

Develop Probability Distribution

A technician services machines as companies in the Phoenix area. Depending on the type of malfunction, the service call can take exactly 1, 2, 3, or 4 hours. The different types of malfunctions occur at the same frequency. a. Develop a probability distribution for the duration of a service call. Duration of Call (x) f(x

Probabilities and Confidence

1. An important issue facing Americans is the large number of medical malpractice lawsuits and the expenses that they generate. In a study of 1228 randomly selected medical malpractice lawsuits, it is found that 856 of there were later dropped or dismissed (based on data from the Physician Insurers Association of America). a)

Calculating mean profit and probability using simulation

Develop a worksheet simulation for the following problem. The management of Madeira Manufacturing Company is considering the introduction of a new product. The fixed cost to begin the production of the product is $30,000. The variable cost for the product is uniformly distributed between $16 and $24 per unit. The product will se

Quality Assurance and Binomial Distribution

John Rengel is the Quality Assurance Supervisor for Vino Supremo Vinyards. He knows that 10 percent of each box of corks is undersized. a) If he were to randomly select 120 corks from the next box, then how many of these corks would John expect to be undersized? b) If he were to randomly select 120 corks from each box,

Probability Distributions Problem

Determine whether each of the distributions given below represents a probability distribution. Justify your answer so I am able to see how this was done. :) (A) x 1 2 3 4 P(x) 1/12 5/12 1/3 1/12 (B) x 3 6 8 P(x) 2/10 .5 1/5 (C) x 20

Probability of a score

2. Assume that the mean SAT score in Mathematics for 11th graders across the nation is 500, and that the standard deviation is 100 points. Find the probability that the mean SAT score for a randomly selected group of 150 11th graders is between 470 and 530. Please show all work for me to better understand how it was done.