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Sample Stats Questions

Please show all work and some explanation as to why you chose the formula you did. Part 1. In some countries, girls are valued much less than boys. Sometimes women in such countries abort fetuses known to be girls and many girl babies are victims of infanticide. Suppose there are 43 girls to every 57 boys who reach age 1 in

Cancer Rate Probability

The reported cancer rate for women subjects is 17%, and the reported cancer rate for men subjects is 23%. 220 women and 250 men were selected independently at random. Find the probability that the difference in cancer percentages between men and women will be greater than 5%.

Moment generating functions and limit theorems

Problems on moment generating functions --------------------------------------- 1. Let X and Y be independent normal rv's, each with mean mu and variance sigma^2. Use moment generating functions to show that X+Y and X-Y are independent normal rv's. 2. If X and Y are independent and M_X(t)=exp{2e^t-2} a

Application of binomial probability in waiting time

You are manager of bank and you want to make sure customers do not have an overly long wait for a customer representative (other than the ATM or deposit box which requires no employee interaction). You know historically for each customer there is a X% chance a customer will walk in and will need customer service. You are going t

Are E1 and E2 mutually exclusive? What is the probability of exactly two girls? Find a recurrence relation and initial conditions that generate a sequence that begins with the given term.

Suppose a coin is flipped and a die is rolled. Let E1 denote the event "the coin shows a tail", let E2 denote the event "the dies shows a 3", and let E3 denote the event "the coin shows heads and the die shows an odd number". Are E1 and E2 mutually exclusive? A family of four children. Assume that it is equally probable

Die, Card and Cash in Hand Game Probabilities

One fair die is rolled. What is the probability of getting an even number? A card is selected at random from an ordinary 52-card deck. What is the probability that it is a heart? In the Maryland Cash In Hand game, to win the grand prize the contestant must match seven distinct numbers, in any order, among the numbers 1 t

Probability of Picking a Company with Nuclear Difficulties

Have to pick 3 out of 7 companies. 2 of the 7 companies will have nuclear difficulties. Please answer: - Chance of not picking a company with nuclear difficulties. - Chance of picking two companies with nuclear difficulties. - Chance of picking one company with nuclear difficulties.

Probability Distribution Binomial

Question(1): A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. a. Compute the probability that two or fewer will withdraw. b. Compute the probability that exactly four will withdraw. c. Compute the probability that

Probability questions: accident rates for drivers in different age groups

An auto insurance agency was investigating accident rates for drivers in different age groups. The following contingency provides a joint probability distribution for drivers by age group and accident rate. a) What is the probability that a randomly selected person from the above group has had more than one accident regardle

Level of data, data descriptions

1. You would like to help some of your math-deficient friends understand probability before they loose too much on lottery tickets. After shuffling two decks of cards, you lay down 40 of them. You say that there should be 10 in each of the four suits: hearts, diamonds, spades, and clubs. What you actually get is 9 hearts, 8 di

Expected Value and Moment Generating Function

1) Type i light bulbs function for a random amount of time having mean mui and standard deviation sigmai, i=1,2. A light bulb randomly chosen from a bin of bulbs is a type 1 bulb with probability p, and type 2 with prob. (1-p). what is the expected value and the variance of the lifetime of this bulb? 2) Mx(t)=exp{2(e^t)-2

IQ Score Distribution

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected adult has an IQ between 110 and 120 (referred to as bright normal)

Probability based on Normal distribution..

Assume that human body temperatures are normally distributed with a mean of 98.20ºF and a standard deviation of 0.62 ºF. a. Bellevue Hopistal in New York uses 100.6ºF as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage

Independent events

A fair die is rolled twice. Suppose A= The first roll shows an even number B= The second roll shows an odd number C= The two rolls show different numbers Prove or disprove that A,B,C are mutually independent events


On an average, 9 trucks arrive per day at a trucking depot. What is the probability that each day next week, six or more trucks will arrive at the depot?

Binomial Probability Distributions

Three unrelated people go for dinner to a Chinese restaurant which uses MSG in its food. Each person has a 10% probability of developing an adverse reaction to the MSG. Let X be the number of people among the three that do develop an adverse reaction. Find the distribution of X.

Exponential distribution

The mileage that car owners get from a specific type of radial tire has an exponential distribution. 50% of the car owners get a mileage greater than 30,000 miles. What percentage of the car owners get a mileage greater than 60,000 miles?

Binomial Probability Distribution for a Procedure's Yield

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. n = 10, x = 2, p = 1/3

Expected Profit Using Probability

A contractor is considering a sale that promises a profit of $31,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $13,000 with a probability of 0.3. What is the expected profit?

Clinical Tests and Headaches

The probabilities were obtained by entering the values of n = 6 and p = 0.167. In a clinical test of the drug lipitor, 16.7% of the subjects treated with 10mg experienced headaches. In each case, assume that 6 subjects are randomly selected and treated with 10 mg of atorvastatin, then find the indicated probability. Binomia

5 Assorted Probability Questions

1. For a particular group of taxpayers, 25 percent of the returns are audited. Six taxpayers are randomly selected from the group. a. What is the probability two are audited? b. What is the probability two or more are audited? 2. On the average an artist sells two of her works per hour at weekend art shows.

Multiplication Rule and Sample Spaces in Probability

A test consists of multiple-choice questions, each having four possible answers (a,b,c,d) one of which is correct. Assuming that you guess the answers to six such questions. a.) Use the multiplication rule to find the probability that the first two guesses are wrong and the last four guesses are correct. That is, find P (WWC

Probability of Guessing a Combination Lock on the First Try

A typical "combination" lock is opened with the correct sequence of three numbers between 0 and 49 inclusive. (A number can be used more than once.) What is the probability of guessing those three numbers and opening the lock with the first try?

Probability Questions

Prepare answers to the following assignments: 1. Sixty percent of the students at Scandia Tech drive to class and 30 percent have GPAs of at least 3.00. Ten percent of the students have a 3.00 GPA and drive to class. If we select a student at random, what is the likelihood that the student had a 3.00 or drives to class?

Quantitative Analysis for Jim's Management Decision

Jim Sellers is thinking about producing a new type of electric razor for men. If the market were favorable, he would get a return of $100,000, but if the market for this new type of razor were unfavorable, he would lose $60,000. Since Ron Bush is a good friend of Jim Sellers, Jim is considering the possibility of using Bush Ma