In this exercise, determine whether a probability distribution is given. In the case where a probability distribution is not described, identify the requirements that are not satisfied. In the case where a probability distribution is described, find its means and standard deviation. Mortality Study For a group of four men,
Mean time between failures (MTBF) of 1200 operating hours. A mechanic wishes to know, "What is the probability that a particular engine may actually reach 1950 operating hours before failing?" As the quality engineer with responsibility for this particular part, what do you calculate for the answer to the question? Show the
Given 5,000 light bulbs from an outside supplier. If past performance data indicates that these have been 3% defective, and a random sample of 40 parts are drawn from the shipment what is the probability that you will find more than 2 defective parts? Use the Poisson distribution to answer this question.
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
A survey showed that 24% of college students read newspapers on a regular basis and that 81% of college students regularly watch the news on TV. The survey also showed that 21% of college students both follow TV news regularly and read newspapers regularly. (a) What is the probability that a randomly selected college student
It was reported that approximately 45% of all university professors are extroverted. Suppose you have classes with 6 different professors. a) What is the probability that all 6 are extroverts? b) What is the probability that none of your professors are extroverts? c) What is the probability that at least 2 of your prof
Does crime Pay? The FBI Standard Survey of Crimes showed that for about 80% of all property crimes , the criminals are never found and the case is never solved. Suppose that a neighborhood district in a large city has repeated property crimes, not always by the same criminals. The police are investigating six property crimes cas
Accidents at a chemical plant occur at a rate of 1.9 per month. Find: The expected number of accidents in a year? The probability of no accidents next month? The probability of fewer than three accidents next month?
The quality control inspector of a production plant will reject a batch of syringes if 2 or more defective syringes is found in a random sample of 8 syringes taken from the batch. Suppose the batch 1% defective syringes. a. Make a histogram showing the probabilities of r = 0,1,2,3,4,5,6,7 or defective syringes in a random sam
James Burke claims that about 70% of all single men would welcome a women taking the initiative in asking for a date. A random sample of 20 single men were asked if they would welcome a women taking the initiative in asking for a date. What is the probability that come a women taking the initiative in asking for a date. What is
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
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)
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
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
Can please show that the Binomial(n, p) family is an exponential family.
A production line manager, J, is trying to design a manufacturing line, using the machines that her company already has. Based on the historical records, each individual candidate machine will fail, during the production, with a probability of 1-p, and their failures are independent. Since the company plans to discard the machin
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
Data collected from town A shows that 60% of drivers are above 30 years old. 5% of all the drivers over 30 will be prosecuted for a driving offense during a year, compared with 10% of drivers aged 30 or younger. If a driver has been prosecuted, what is the probability they are 30 or younger?
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
I scheduled three calls for a particular day, and each call has a probability of 0.5 of making a sale. What are his probabilities of making (a) three sales, (b) two or more sales, (c) no sales?
An oil co. is drilling some wells. the results are described as either a dry well or a producer well. Past experience suggests that 10% of exploratory wells are producer wells. If the company drills 12 wells, what is the probability that all 12 wells are producer wells? What is the probability that all 12 wells are dry wells?
A foreman for a firm admits that on 10% of his shifts he forgets to shut off the machine. This causes the machine to overheat and the probability that a defective mold will be produced during the early morning run increases from 2% to 20%. Draw a probability tree that represents this information and use it to calculate the pro
People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7% of the American population have O-negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor? (Please show all steps)
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
In the cash now lottery game there are 10 finalists who submitted entry tickets on time. From these 10 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the second prize is one hundred thousands dollars, and the third prize is ten thousand dollars. Use the permutations rule to determine th
You roll two fair dice, a green one and a red one. a) Are the outcomes on the dice independent? b) Find P(1 on green die and 2 on red die). c) Find P (2 on green die and 1 on the red die). d) Find P(1 on green die and 2 on red die) or (2 on green die and 1 on red die).
Find the probability that a standard normal random variable will assume a value between: a. z = 1.5 and z = .75 b. Greater than 1.25 c. Find a z such that 70% of the area is above that value.
Elementary Probability Theory: A botanist has developed a new hybrid cotton plant that can withstand insects better than other cotton plants. However, there is some concern about the germination of seeds from the new plant.To estimate the probability that a new plant will germination, a random sample of 3000 seeds was planted
a) If you roll a single fair die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely? b) Assign probabilities to the outcomes of the sample space of part? a)do the probabilities add up to 1 ? c) What is the probability of getting of getting a number less than
The port of Trop can service only 1 ship at a time. However, there is mooring space for 3 more ships. Trop is a favorite port of call, but, if no mooring space is available the ships have to go to the next port. An average of 7 ships arrive each week, according to the Poisson process. The Port of Trop has the capacity to handle