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# Probability

### Binominal Distribution: Probability

In a certain binomial distribution, &#960; = 0.20 and n = 30. In using the normal approximation, a. What are the mean and standard deviation of the corresponding normal distribution? b. If x = the number of "success" among the 30 observation, determine the following: P(x = 5), P(4 &#8804; x &#8804; 7), P(1 &#8804; x &#8804;

### Probability: Take the Order or Not?

My youngest brother used to own a cafe in Calgary and I visited him frequently for free meals. One day, Indiana Jones rushed in and wanted to order two dozen roasted chickens. But there was a catch. He insisted that all the chickens should be heavier than 5.5 lbs, or else my brother would face very serious consequences.

### Normal distribution A software company finds that the average number of errors in its software per 1000 lines of code is 4 with standard deviation equal to 0.5. Use the 68-95-99.7 rule to calculate the following values: a)Almost all (99.7%) 1000 lines of code contain a number of errors that varies in what range of values? b)The percentage of samples of 1000 lines of code that contain between 3 and 5 errors. c)The percentage of samples of 1000 lines of code that contain less than 2.5 errors. d)The 2.5th percentile of the distribution of the number of errors per 1000 lines of code.

A software company finds that the average number of errors in its software per 1000 lines of code is 4 with standard deviation equal to 0.5. Use the 68-95-99.7 rule to calculate the following values: a)Almost all (99.7%) 1000 lines of code contain a number of errors that varies in what range of values? b)The percentage of

### Binomial process and probabilities

It has been estimated that 17.0% of mutual fund shareholder are retired persons. Assuming the population proportion to be &#960; = 0.17 and that a simple random sample of 400 shareholders ha been selected: a. What is the expected value of p = the proportion of those in the sample who are retired? b. What is the standard error

### Probability of standard normal table

Using the standard normal table, find the following probabilities associated with z: a. P(0.00 ≤ z ≤ 1.25) b. P(-1.25 ≤ z ≤ 0.00) c. P(-1.25 ≤ z ≤ 1.25) Using the standard normal table, find the following probabilities associated with z: a. P (-0.36 ≤ z ≤ 0.00) b. P(z ≤ -0.36) c. P(z ≥ -0.43)

### The Probability of Overbooking Flights

Please help with the following problem involving statistics and probability. Air America is considering a new policy of booking as many as 400 persons on a airplane that can seat only 350. (Past studies have revealed that only 85% of the booked passengers actually arrive for the flight.) Estimate the probability that if Ai

### BrainMass Expert's Approach to: Statistics - All Topics

A contractor must pay a \$40,000 penalty if construction of an expensive home requires more than 16 weeks. He will receive a bonus of \$10,000.00 if the home is completed within 8 weeks. Based on experience with the type of project, the contractor feels there is a 0.2 chance the home will require more than 16 weeks for completion,

### Probability: City Law-Enforcement Official

1. A city law-enforcement official has stated that 20% of the items sold by pawn shops within the city have been stolen. Ralph has just purchased 4 items from on of the city's pawn shops. Assuming that the official is correct, and for x = the number of Ralph's purchases that have been stolen, determine the following: a. P(x

### Knowledge about Statistics - All Topics

Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6 in. and a standard deviation of 1.0 in. (based on anthropometric survey from Gordon, Churchill, et al.). a. If one male is randomly selected, find the probability that his

### Calculating Expected Return

I am planning on building an airport. There are only two parcels, labeled A and B on which the airport could feasibly be built. A corp. knows that once a parcel is chosen the cost of land near the airport will go up so they are considering buying land for an airport hotel adjacent to one of both of these parcels now before a sit

### Probability ... (Please see the attached document)

1). You are tossing a die that has probability of 1/6 of coming up 1 on each toss. Tosses are independent. We are interested in how long we must wait to get the first 1. (a). The probability of a 1 on the first toss is 1/6. What is the probability that the first toss is not a 1 and the second toss is a 1? (b). What is the pr

### Scenario Questions ... (Please see the attached file)

Pam Beesly, the CEO's Administrative Assistant, has worked for Mr. Rump for a little over one year. She was originally hired by the Chief Operations Officer, Mr. Halpert, as his personal secretary but when the opening for the new assistant to the CEO became available (his last one, Marla, had to leave suddenly due to personal p

### Scenario Questions on Production of DVDs

Chief of Bruin Consulting Engineering Division, Dr. Dil Bert, is in charge of and overseeing the production of the company's DVDs. The DVDs are used to record the company's PSAs and then distributed to the local public access channels. Unfortunately, the Engineering Division's quality control is not up to the standards that th

### Basic probability questions involving intersections of events and events that are either independent events or mutually exclusive events.

Mr. Arthur Van De Lay, not only the company's Chief Information Officer, but also the reigning mid-west "Rock, Paper, Scissors" champion, has bid on two eco-friendly projects. Project "A" is a recycling of metals contract with the town of Bellevue, NE, and project "B" is the toxic clean up contract for Omaha, NE, city parks aft

### Interpretations of probability

Please see the attached file. 1) The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1, 0.2, 0.4, and 0.2 respectively. Let A denote the event {a, b, c} and B denote the event {c, d, e}. Determine the following: a) P(A) b) P(B) c) P(A') d) P(A U B) e) P(A n B) 2) If the last digit

### Determining Whether a Jury Selection Process Is Biased

Determining Whether a Jury Selection Process Is Biased Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to Table 5-1 and find the indicated probability. a. Using the probability values in Table 5.1, find the probability value that should be used for determi

### Find binomial probabilities

Population of consumers where 30% of them favored a new product and 70% of them disliked it. If 20 persons are sampled, what are the probabilities of finding: Binomial: 8 or fewer consumers who favor the product. Precisely 10 consumers who favor the product. Fewer than 6 consumers who favor the product. More than 7 consumers who

### Binomial probabilities - Trevor is interested in purchasing the local hardware/sporting goods in the small town of Dove creek, Montana. After examing accounting records for the past several years, he found that ...

Trevor is interested in purchasing the local hardware/sporting goods in the small town of Dove creek, Montana. After examing accounting records for the past several years, he found that the store has been grossing over \$850 per day about 60% of the business days it is open. Estimate the probability that the store will gross over

### Random variables and probabilities distributions

Age range(yr)| 20-29 30-39 40-49 50-59 60-69 70-79 80+ Midpoint | 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of | 5.7 9.7 19.5 29.2 25.0 9.1 1.8 nurses a) Using the age midpoints x and the percentages of of nurses, do we have a valid probability distribution? Explain. b)

### Statistics - Probability Questions

1.Typographical and spelling errors can be either "nonword errors" or "word errors." A nonword error is not a real word, as when "the" is typed as "teh." A word error is a real word, but not the right word, as when "lose" is typed as "loose." When undergraduates are asked to write a 250 word essay (without spell checking), the

### Normal Distribution - Scores on an examination are assumes to be normally distributed with mean 78 and ... (Please see the attached document)

Please solve the following problem: Scores on an examination are assumes to be normally distributed with mean 78 and variance 36. a.What is the probability that a person taking the examination scores higher than 72? b.Suppose that students scoring in the top 10% of this distribution are to receive an A grade. What is th

### Pedestrian Walk Buttons (Probability) - Pedestrian Walk Buttons New York City has 750 pedestrian walk buttons that work, and ...

Pedestrian Walk Buttons New York City has 750 pedestrian walk buttons that work, and another 2500 that do not work (based on data from "For Exercise in New York Futility, Push Button," by Michael Luo, New York Times). If a pedestrian walk button is randomly selected in New York City, what is the probability that it works? Is

### Probability(Combinations)

Question: An office furniture manufacturer makes filing cabinets. It offers customers 2 choices for the base and 4 choices for the top, and 5 different heights. A customer may choose any combination of the 5 different-sized modules so that the finished filing cabinet has a base, a top, and 1, 2, 3, 4, 5, or 6 storage module

### Probability - Genetics Cystic fibrosis is a recessive trait

Cystic fibrosis is a recessive trait in humans. a. If two people are heterozygous for cystic fibrosis and they have 3 kids, what is the probability that one of these will have cystic fibrosis? b. What is the probability that only the first child will have cystic fibrosis? c. What is the probability that they will hav

### Investment/maxium probability One of your friends has \$ 2000.00 available to invest. Assume that all the money must be placed in one of three investments; a money market fund, a stock, or gold. Each dollar that your friend invests in the money market fund earns a virtually guareanteed 12%. Each dollar that is invested in stock earns an annual return characterized by the probability distribution provided. Each dollar that is invested in gold earns an annual return characterized by the probability distribution provide. A) If your friend must place all the available funds in a single investment, which investment should he choose to maximize his expected earnings of the next year?

Please see the attached file(s). Problem One of your friends has \$ 2000.00 available to invest. Assume that all the money must be placed in one of three investments; a money market fund, a stock, or gold. Each dollar that your friend invests in the money market fund earns a virtually guareanteed 12%. Each dollar that is

### Short Problems in Probability

1. A furniture manufacturer offers bookcases in 5 different sizes and 3 different colors. If every color is available in every size, then the total number of different bookcases is A) 5 B) 8 C) 15 D) 30 2.A certain system has two components. There are 10 different models of the first component and 10 different of the

### Find a percentile from a known normal probability distribution

Please help with the following problem. A newspaper article reported that people spend a mean of 6 hours per day watching TV, with a standard deviation of 1.9 hours. A psychologist would like to conduct interviews with the 15% of the population who spend the most time watching TV. She assumes that the daily time people spe

### Quantative Research Methods - 36. An investment will be worth \$1,000, \$2,000, or \$5,000 at the end of the year. The probabilities of these values are .25, .60, and .15, respectively. Determine the mean and variance of the worth of the investment. ... [Please the attached questions file.]

36. An investment will be worth \$1,000, \$2,000, or \$5,000 at the end of the year. The probabilities of these values are .25, .60, and .15, respectively. Determine the mean and variance of the worth of the investment. 39. A Tamiami shearing machine is producing 10 percent defective pieces, which is abnormally high. The qual

### Probability Problem of Big Ten University

An alcohol awareness task force at Big-Ten university sampled 20 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained. Did Well on Midterm

### Probability: Calculating the Odds

Question: If a person were to be hit by lightning, they have a 33 percent chance of being killed. (a) Find the odds that a person will be killed if struck by lightning. (b) Find the odds against a person being killed if struck by lightning.