Define probability distributions. Describe two common probability distributions. Looking for a good original (yet cited) response to this definition. And if you can describe two common ones with an example for each that would be great.
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
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
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
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
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
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
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)?
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
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
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?
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
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
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)
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
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,
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
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.
4.182: For each of the following examples, decide whether x is a binomial random variable and explain your decision. (see examples attached). 4.184: Consider the discrete probability distribution shown here. x 10 12 18 20 p(x) .2 .3 .1 .4 a) Calculate mean, varian
1. Explain the difference between descriptive and prescriptive (optimization) models. 2. Describe how to use Excel data tables, scenario manager, and goal seek tools to analyze decision models. 3. Explain the purpose of Solver and what type of decision model it is used for. 4. What approaches can you use to incorporate uncert
1. Let X be a random variable with probability density function given by f(x) - 2(1 - x), 0 <= x <= 1, 0, otherwise a. Find the density function of Y - X^2 b. Find the mean and variance of Y. 2. Let X be a random variable with probability density distribution given by f(x) - x, 0 <= x <
1. Determine for the following box, whether number and shape are independent or dependent. The box has a triangle with a 3 in it, a square with a 2 in it, a square with a 3 in it, and a triangle with a 2 in it. a. dependent b. independent 2. There are 5 Democrats, 18 Republicans, and 14 Independents in a room. Two peopl
86. Give the z-score for a measurement from a normal distribution for the following: a. 1 standard deviation above the mean b. 1 standard deviation below the mean c. equal to the mean d. 2.5 standard deviations below the mean e. 3 standard deviations above the mean 118. Suppose x is a binomial random vari
38. Suppose x is a binomial random variable with n = 3 and p = 3 a. calculate the value of p(x), x = 0,1,2,3 using the formula for a binomial probability distribution b. using your answers to part a, give the probability distribution for x in tabular form 42. The binomial probability distribution is a family of proba
2. Security analysts are professionals who devote full time efforts to evaluating the investment worth of a narrow list of stocks. The following variables are of interest to security analysts. Which are discrete and which are continuous random variables? a. the closing price of a particular stock on the New york stock exc
48. For two events, A and B, P(A) = 0.4, P(B) = 0.2, and P(A/B)=0.6 a. find P(A and B) b. find P(B/A) 50. An experiment results in one of three mutually exclusive events, A,B, or C. It is known that P(A) =.30, P(B) = .55 and P (C) = .15. Find each of the following probabilities: a. P(A U B)
Let F(t) = 1- e ^(- lamda*t) a) Show how to generate a random variable from the exponential distribution function shown above. Show derivation of the equation. b) Generate 10000 random variables X and Y with cumulative distribution F(t); do this twice using lambda =2,3 (so 2 columns of 10000 numbers each). c) Using the equa
We have 7 boys and 3 girls in our church choir. There is an upcoming concert in the local town hall. Unfortunately, we can only have 5 youths in this performance. This performance team of 5 has to be picked randomly from the crew of 7 boys and 3 girls. a. What is the probability that all 3 girls are picked in this team of 5?
Two marbles are selected, one at a time from a jar of marbles containing 10 black, 10 brown, 10 white and 10 green marbles. Let x represent the number of white marbles selected in 2 separate selections from the jar. (A) If this experiment is completed without replacing the marbles each time, explain why x is not a binomial
1. If the IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. (a) Find the probability that a randomly selected person has an IQ score between 88 and 112. (Show work) (b) If 100 people are randomly selected, find the probability that their mean IQ score is greater than 103. (Show work) 2.