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# Probability

### A famous restaurant owner noticed that in the past 20 years his hamburger supply shows a normal distribution in weight...

A famous restaurant owner noticed that in the past 20 years his hamburger supply shows a normal distribution in weight. Average weight was 10.0 ounces with a standard deviation of 0.3 ounces after they were cooked. (Consider normal distribution) * What is a probability that a customer gets a hamburger that weighs at least 1

### Mean Height of 70 Women Sampling Distribution

(See attached file for full problem description) The mean height of women in a certain population (ages 20-29) is mu = 66 inches. A random sample of 70 women in this age group is selected. What is the probability that the mean for the sample, is greater than 66.8 inches? Assume sigma = 2.75 inches. --- PLEASE USE EXCEL F

### Probability of continuous distributions

1- The accounting department at Weston Materials, Inc., a national manufacturer of unattached garages, reports 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

### Probability and Random Selection

1) When writing about the probability that it will rain in Boston on July 4 of next year, a newspaper reporter states that the probability is 1/2, because either it will rain or it will not. Is this reasoning correct? 2) In a recent year, 389 of the 281,421,906 people in the United States were struck by lighting. Estimate t

(1) An instructor obsessed with the metric system insists that all multiple-choice questions have 10 different possible answers and only one is correct. What is the probability of answering correctly if a random answer is picked? An event is unusual if probability is 0.05 or less, so is it unusual to answer the question by c

### Computer chips and probability

Computer company makes computer chips. Chips made with a 27% yield, meaning that 27% of them are good and the rest are defective. 1. If one chip is picked randomly, find the probability that it is not good. 2. If 2 chips are randomly picked, find the probability that they are both good. 3. If 5 chips are picked randomly

### Probability and weight distribution of caught fish

Going fishing in a lake with bass weighing an average of 3 pounds with a standard deviation of 0.3 pounds 2 fish caught. What is the probability that both catches were 3.5 pounds or heavier? 4 fish caught with 2 of them in the lowest 20% of the weight distribution. Other 2 were in the top 10% of weight distribution. Estim

### Seven households and other questions

Seven households have the following number of creatures living there, 6,5,8,9,7,8,9. The standard deviation of creatures living in these households? Give the five number summary of distribution for creatures living in these houses. --- 30% of people own a house with one garage, 40% own a house and parking space,

### Probability Problem Set on Estimation and Likelihood

1)When writing about the probability that it will rain in Boston on July 4 of next year, a newspaper reporter states that the probability is ½, because either it will rain or it will not. Is this reasoning correct? 2)In a recent year, 389 of the 281,421,906 people in the United States were struck by lighting. Estimate the

### Simulation of random numbers using STATDISK

Probabilities through Simulations 1)Dice Simulation - Use Statdisk to simulate 1000 rolls of a pair of dice. Sort the results, then find the number of times that the total was exactly 7. ___________. Based on that result, estimate the probability of getting a 7 when two dice are rolled._____________. How does this es

### Probability

66. Ninety students will graduate from Lima Shawnee High School this spring. Of the 90 students, 50 are planning to attend college. Two students are to be picked at random to carry flags at the graduation. a. What is the probability both of the selected students plan to attend college? 1. P (A) + P (B) = b. What is the

### Jerry can open up a small shop, large shop, or no shop

Jerry can open up a small shop, large shop, or no shop. There will be a 5 year lease on a building he wants to make the correct decision. Jerry is also thinking about hiring a consultant to conduct a market research study. If the study is conducted, the results could be either favorable or unfavorable. Develop a decsion tree

### Determining Amount of Cheese to Manufacture

Jason must decide how many cases of cheese to manufacture each month. The probability that the demand will be 6 cases is 0.1, for 7 cases is 0.3, for 8 cases is 0.5, and for 9 cases is 0.1. The cost of each case is \$45 and the price Jason gets for each case is \$95. Any case not sold by the end of the month is of no value due to

### Probability questions: Gaussian approximation and Poisson approximation

Probability: 1.You flip a coin n times.Please answer the following questions about the fraction f of the tosses that show heads. A. Lets say n=100. Compute exactly the prob that the fraction of the coins showing heads is f=0.5 B. Say n=100 and consider the prob that f=0.5. Show that this probability can be approximated us

### Statistics question

Suppose that during a football game, lemonade sells for \$15 per gallon but only costs \$4 per gallon to make. If they run out of lemonade during the game, it will be impossible to get more. On the other hand, leftover lemonade has a negligible value. Assume that you believe the fans would buy 10 gallons with probability 3/10, 11

### Gaussian limit of binomial distribution

In the attachment this problem is formulated in terms of noninteracting particles.

### Decision Tree and Statistics

I need some help with this question containing a decision tree and analysis: Bob is a second year MBA student contemplating his employment situation. He has three prospects: • He has a "standing" offer from Company A for \$65K. This offer does not expire. • He has an "exploding" offer from Company B for \$75K. This offe

### Calculations for Probability

1. For each of the following stats, prove the below or give counterexamples: a. If 2 events A & B are independent, then A & B' are also independent. b. Let's say that 3 events A,B,C have probabilities satisfying P(ABC)=P(A)P(B)P(C),then the events A & B are independent. c. If P(A|B)>P(A), then P( A|B' )< P(A). (you may assume

### Binomial distribution and how many ways

(See attached files for full problem description) 1. A pizza shop offers twenty toppings. No topping is used more than one. In how many ways can a six-topping pizza be formed? 2. Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.

### Probability Distribution Theory

Find the distribution function. See attached file for full problem description.

### probability of rolling two fair dice

(See attached file for full problem description) Two fair dice have both had two of their sides painted red, two painted black, one painted yellow and one painted white. (a) when this pair of dice is rolled, what is the probability that both will show the same color? (b) What is the probability that only one of the dice wil

### Calculating probability for exponential distribution

Suppose a worker needs to process 400 items. The time to process each item is exponentially distributed with a mean of 2 minutes, and the processing times are independent. Approximately, what is the probability that the worker finishes in less than 7 hours?

### Poisson Random Variable

Let X be a Poisson random variable with parameter 5, and let Y = min(X,5). (a) What is the p.m.f. of X? (b) What is the mean of X? (c) What is the variance of X? (d) What is the p.m.f. of Y (e) Compute E[Y}.

### Problems on Basic Probability

8. A sample of 2,000 licensed drivers revealed the following number of speeding violations. Number of Violations Number of Drivers 0 1,910 1 46 2 18 3 12 4 9 5 or more 5 Total 2,000 1. What is the experiment? 2. List one possible event. 3. What is the probability that a particular driver had

### Random Probability and Statistics

1. Each vehicle in Mexico is either a truck, car or bicycle. Also each vehicle is red, green or yellow. We pick a vehicle at random. The following are known facts: 1. There's a 30% chance that vehicle is truck 2. There's 50% chance that vehicle is red 3. There's 20% chance that vehicle is a red truck 4. The vehicle is

### Chances of making a sale on a phone call

Assume the probability that you will make a sale on any given phone call is 0.78. Find the probability that you (a) make your first sale on the 4th call, (b) make your first sale on the first, second, third, or fourth call, and (c) you do not make a sale on one of the first 4 calls.

### PiggyBank required sample size

Piggy Bank would like to examine the required sample size needed to be able to estimate the mean dollars that each card holder will spend each month. It would like to be within plus or minus \$10 of the true mean with a 98% confidence level. The standard deviation is thought to be \$500. How many card holders should be sampled? Af

### Collectively exhaustive event

Concerning the problem below, I understand that one event must occur to have collectively exhaustive event. I don't understand how to determine the problem as stated. If two events are collectively exhaustive, what is the probability that both occur at the same time? a. 0 b. 0.50 c. 1.00 d. Can't be determined from the i

### Critical Flight Paths

Two airlines offer conveniently scheduled flights to the airport nearest your corporate headquarters. Historically, flights have been scheduled as reflected in this transition matrix. Current Flight Next Flight Airline A Airline B Airline A .6 .4 Airline B .2 .8 If your last flight was on B, what is the probabili

### Solving Various Probability Problems

(See attached file for full problem description) --- 1. A food distributor carries 64 varieties of salad dressing. Appleton Markets stocks 48 of these flavors. Beacon Stores carries 32 of them. The probability that a flavor will be carried by Appleton or Beacon is 15/16. Find the probability a flavor is carried by both A