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Discrete Probability Distributions

1. A researcher calculates the expected value for the number of girls in five births. He gets a result of 2.5. He then rounds the result to 3, saying that it is not possible to get 2.5 girls when five babies are born. Is this reasoning correct? 2. A researcher reports that when groups of four children are randomly selected

Probability of attaining different grades in a statistics class.

In a large section of statistics class, the points for the final exams are normally distributed with a mean of 72 and a standard deviation of 9. Grades are to be assigned according to the following rule. 1) the top 10% receive A 2) the next 20% receive B 3) the middle 40%receive C 4) the next 20% receive D 5) the bott

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

Three questions about probability

(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

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,

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


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

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

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

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

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

Sample Probabilities

In a city, 60% of the voters are in favor of building a new park. An interviewer intends to conduct a survey. a. If the interviewer selects 20 people randomly, what is the probability that more than 15 of them will favor building the park? b. Instead of choosing 20 people as in part a, suppose that the interviewer wants t

Exponential Distribution to Determine Product Lifetimes for two Products

A consumer is contemplating the purchase of a new compact disc player. A consumer magazine reports data on the major brands. Brand A has lifetime (TA) which is exponentially distributed with m=.02; and Brand B has lifetime (TB) which is exponentially distributed with m=.01. (The unit of time is one year). a. Find the expec

Probability Generating Function

Let X1, X2,... be i.i.d. random variables with p.g.f Gx(s) and N be a r.v independent of X with p.g.f. Gn(s). Define S=X1+X2+...+XN. Find Var(S) in terms of expectations and variances of X and N.

Blonde hair probability problem

In a sample of 2400 people, 170 have blonde hair. Two unrelated people are selected at random... (See attached file for full problem description)

Quality Management

(See attached file for full problem description) --- 1. A study determines that 60% of the voters in a town intend to vote for the incumbent mayor. If a sample of 8 people is selected, the approximate probability that 6 of the 8 people surveyed intend to vote for the incumbent is (using the binomial probability formula): a.

Simple Probability Problems

1. Suppose you have 3 nickels, 2 dimes, and 6 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that a. You will draw a dime? b. You will draw a half-dollar? c. You will draw a quarter? 2. You are rolling a pair of dice, one red and one green. What is the probability

Subjective Probability of a Capital Investment Firm

Suppose that an executive of a venture capital investment firm is trying to decide how to allocate his funds among three different projects, each of which requires a $100,000 investment. The projects are such that one of the three will definitely succeed, but it is not possible for more than one to succeed. Looking at each p

Probability problem marginal analysis

Working on below problem to identify error as presented. "On the fictitious game show "Marginal Analysis for Everyone" the host subjects contestants to unusual tests of mental skill. On one, a contestant may choose one of two identical envelopes labeled A and B, each of which contains an unknown amount of money. The host

Word Problem for probability ratio

Trying to complete the below word problem but not sure how to solve. ________________ It is said that Napoleon assessed probabilities at the battle of waterloo in 1815. his hopes for victory depended on keeping the English and Prussian armies seperated. Believing that they had not joined forces on the morning of the fatefu

Blossom's Flowers purchases roses for sale for Valentine's Day

Blossom's Flowers purchases roses for sale for Valentine's Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine's Daycan be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses: 100, 200 or 400 dozen roses. Given 0.2, 0.4 and 0.4 are the probabilities fo

A survey of 400 customers was completed in an attempt to measure the number of cups of coffee ordered during business hours versus those ordered during non-business (pleasure) hours. They also recorde

A survey of 400 customers was completed in an attempt to measure the number of cups of coffee ordered during business hours versus those ordered during non-business (pleasure) hours. They also recorded how many items were purchased during the transaction. Results are as follows: Customer 0 extra 1 extra 2 extra 3 or more Tota