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# Probability

### what is the probability that three labs will detect drugs

Employee drug testing is done in the following manner. An employee is chosen at random and a urine specimen is taken. The specimen is divided into three vials and each vial is sent to an independent lab. If each lab has a 0.97 probability of detecting illegal drugs when they are present, what is the probability that all three la

### Joint and marginal probabilities for a sample from a deck of cards

You have a standard deck of cards and you take out 2 cards at random. Let Y1 represent the number of red Queens in your sample and let Y2 represent the number of spades in your sample. a) calculate p. it is mean p(Y1, Y2); b) calculate var (Y1I Y2=1) c) Determine E (Y2I Y1=0)

### Statistics: Joint, marginal and conditional densities & expectation

** Please see the attached file for a Word formatted copy of the problem ** 1. Consider the joint pmf p(x,y)=cxy, 1<x<y<3. a) Find the normalizing constant c. b) Are X and Y independent? Prove your claim. c) Find the expectations of X, Y, XY. 2. Conceptual Suppose (X, Y) have the joint pmf p(x, x+1) = 1/(n+1), x= 0,1,2

### Deriving Discrete Uniform Distribution Formulas

Let Y take on the values 1, 2....., n; all of these values ov Y are equally likely. this probability distribution is called the discrete uniform distribution. a) Derive the formula for the expected value Y, b) Derive the formula for the moment generating function of Y

### Probability

1. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use a binomial probabilities table to find the probability of x successes given that probability p of successes on a given trial when: n=2, X=0, and p=.90 2. Three cards selected from a standard 52 card deck without replacement. Th

### Probability of Increase Actions

1) A box contain 90 good times and 10 bad items. Thus the probability of randomly choosing a good item from this box is 0.9. A second box also contains 90 good items and 10 bad items. An item is randomly selected from the second box and is placed in the first box. Does this action increase the likelihood of picking a good item

### Probability of random selection with coins

A jar contains a variety of coins. The coins are distributed as follows: 60 pennies 33 nickels 27 dimes 75 quarters For this distribution, find the probability of randomly selecting the following coins: a) a nickel b) a quarter, a dime or a penny c) two quarters or two dimes, with replacemen

### Cleveland Tool Works probability of defective units

A machining operation at Cleveland Tool Works (Process A) produces small parts, 10% of which are defective. A similar operation (Process B) produces small but unrelated parts. Process B is considered to be in control if it produces no more than 10% defective units. Sampling for Process A consists of selecting 20 units at specifi

### Statistics: Probability for Cards

Suppose that a 3 of spades is drawn from a deck of cards. Let A = the event that the next card drawn is a heart and B = the event that the next card drawn is an ace. Is the following statement true or false? Events A and B are independent. a. true b. false

### Probability of Gender and Drinking Level

Non drinker regular drinker heavy drinker total man 135 45 5 185 woman 187 21 13 221 total 322

### Continuous Uniform Distributions

See the attached file. 1. Suppose X ~ U[-2, 2]. For what a,b is a+bX~U[0,1]? 2. A city bus is supposed to arrive at a fixed stop at 12:00 noon, but its arrival time is uniformly distributed between 11:57 AM and 12:04 PM. If it has not yet arrived at 12:01 PM, what is the probability that it will arrive by 12:02 PM? 3. The con

### Statistics

1. A volunteer ambulance service handles 0 to 5 service calls on any given day. The probability distribution for the number of service calls is as follows. Number of Service Calls Probability 0 .10 1 .15 2 .30 3 .20 4 .15 5 .10 a. Is this a valid probability distribution? Why or why not. b. What is the probability o

### Statistics: Population mean, Z scores, mean distribution, probability, normal distribution

Problem Set 2: Chapter 5, problems 6a, 6b, 24, 26; 6. For a population with a mean of µ =100 and standard deviation of ? = 10, a. Find the z-score for each of the following X values. X = 105 X = 120 X = 130 X = 90 X= 85 X = 60 b. Find the score (X value) that corresponds to each of the following z-scores. z = -1.

### probability and expectations

The probability in detecting a crack in an airplane wing= probability of inspecting a plane with a wing crack (P1) x probability of inspecting the details in which a crack is located (P2) x probability of detecting the damage (P3) Find the probability of detecting a crack if (P1=.9, P2=.8 & p3=.5)? If 50 planes are inspected

### Construct a decision tree for medical professionals for constructing a private clinic.

A group of medical professionals is considering the construction of a private clinic. If medical demand is high (i.e. there is a favorable market for the clinic), the physicians could realize a net profit of \$100,000. If the market is not favorable, they could lose \$40,000. Of course, they don't have to proceed at all, in which

### Tree diagram, probability in card selection, math instructors

2. A mini license plate for a toy car must consist of three numbers followed by a letter. Each number must be a 1, 3, or 5. Repetition of digits is NOT permitted. Each letter must be an A, B or C. - Use the counting principle to determine the number of points in the sample space. - Construct a tree diagram to represent this

### Normal Probability: Marathon qualification

7000 people could qualify for a marathon if they complete the 26-mile plus distance in under 3 hours and 10 minutes. 6350 complete the race. The times are normally distributed and the mean is 3 hours and 40 minutes with a standard deviation of 28 minutes. How many runners qualified?

### Normal Probability: English Scores

Scores are normally distributed with a mean of 70 and a standard deviation of 10. The school has decided to place the top 25% into honors English and the bottom 20% into remedial English. What scores separate the upper 25% and lower 20% of the students from the rest? Please explain with solution.

### Statistics: Probabilities in a tennis match

A plays tennis against B. During a given game, the score reaches deuce. Each player then needs to score two more points than the other to win the game. Assuming that each point is independently won by A with probability P, what is the probability they will have to play a total of 2n points to end the game? What is the probabilit

### This solution helps with probability problems

Among the students doing a given course, there are four boys enrolled in the ordinary version of the course, six girls enrolled in the ordinary version of the course, and six boys enrolled in the higher version of the course. How many girls must be enrolled in the higher version of the course if sex and version of the course a

### Counting Principle, Tree Diagram, Probability, Venn Diagram

2. A mini license plate for a toy car must consist of a number followed by two letters. Each letter must be a C, A or R. Each number must be a 3 or 7. Repetition of letters is permitted. Use the counting principle to determine the number of points in the sample space. Construct a tree diagram to represent this situation Li

### Probability function, distribution, value of random variable

Answer the following questions and show your work. 1. Test the following function to determine whether it is a probability function: P(x) = (x²+5)/80 ; for 1,2,3,4, or 5. 2. A small bag of M&M candies has the following assortment: red(10), blue(2), orange(5), brown(12), green(0), and yellow(8). Give the probability dis

### Probability that mean score on aptitude test is between 98 and 102

Assume that the mean score on a certain aptitude test across the nation is 100, and that the standard deviation is 20 points. Find the probability that the mean aptitude test score for a randomly selected group of 150 8th graders is between 98 and 102.

### Probability: Sock Example Problem

A drawer contains 11 identical red socks, and 8 identical black socks. Suppose that you choose 2 socks at random in the dark A) What is the probability that you get a pair of red socks? B) What is the probability that you get a pair of black socks? C) What is the probability that you get two unmatched socks?

### Age distribution in a city; votes for candidate hughes

7.31 Suppose the age distribution in a city is as follows: Under 18 (22%) 18-25 (18%) 26-50 (36%) 51-65 (10%) over 65 (14%) A researcher is conducting proportionate stratified random sampling with a sample size of 250. Approximately how many people should be sampled from each stratum? Do I use the z formula for sample pr

### Statistics: Probability, Tree Diagram

* Please see the attached file for the graph ** Sec 12.7 If the wheel is spun and each section is equally likely to stop under the pointer, determine the probability that the pointer lands on: 20. a number greater than 6, given that the color is red. 28. Mendel Revisited A pea plant must have exactly one of each of t

### Probability of taking a summer vacation this year

Summer Vacation The table shows the results of a survey in which 146 families were asked if they own a computer and if they will be taking a summer vacation this year. a) Find the probability that a randomly selected family is not taking a summer vacation this year. b) Find the probability that a randomly selected family own

### Probabilities, Mean, Variance and Standard Deviation

1. You are warming up with the dice in the lobby of a casino before making your move to the casino floor. Suppose you have two regular 6-sided dice, with sides numbered from 1 to 6 on each die. What is the probability of rolling them both at once, and getting a sum of TEN? Probability = Round your final answer to two decimal p

### Probability of Dives and Sides

See the attached file. ONLY NEED ANSWERS NO WORK NEEDS TO BE SHOWN 1. Suppose that you have two regular 6-sided dice, with sides numbered from 1 to 6 on each die. What is the probability of rolling them both at once, and getting a sum of seven? Express your answer as a decimal and round your final answer to two decimal plac

### Normal approximation to binomial

Components shipped include 0.5% defectives. You plan to select 80 items; if 0 are defective, you will assume all are okay. (Using normal approximation to binomial) a) Find the probability that you will find 0 defectives in 80 items. b) Find the probability you will find none if p = 1.5%