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Probability

Computing probability for normally distributed data

The U.S. Census Bureau announced that the median sales price of new houses sold in April 2008 was $221,600, and the mean sales price was $274,300 (www.census.gov/newhomesales, July 20, 2009). Assume that the standard deviation of the prices is $90,000.

Borel Cantelli Lemma Application

Let X1, X2, and X3,... be independent identically-distributed Poisson (lamda) random variables. What is the value of P[Xn>n i.o.]? Does it depend on the value of lamda? (Be careful to justify your answer.)

Probability of a Flush Draw with an Inside Straight Draw

Suppose you are playing Texas holdem and you hold the 8 and 9 of hearts. The flop comes the 3 of hearts, the jack of spades and the Queen of hearts. You now have an inside straight draw (needing a 10 for a straight) and a flush draw (needing a heart for a flush). a) What is the probability that you hit a straight or a flu

Confidence Interval for Proportion Calculation

According to a report published by the Pew Research Center in February 2010, 61% of Millennial (Americans in their teens and 20's) think that their generation has a unique and distinctive identity (N=527) a. Calculate the 95% confident interval to estimate the percentage of Millennial who believe that their generation has a

Confidence Interval for the Mean of Nervousness

You have been research for your statistics class on how nervous the American adults are in general, you have decided to use HINTS 2007 data set that has a scale (going from 0 to 24)measuring the psychological distress of the respondents. a. According to HINTS 2007 data, the average psychological distress score, for this sample

Integer Programming: Wedding Planning

Elizabeth Bailey is the owner and general manager of Princess Brides, which provides a wedding planning service in Southwest Louisiana. She uses radio advertising to market her business. Two types of ads are available--those during prime time hours and those at other times. Each prime time ad costs $390 and reaches 8,200 people,

13 Probability Statements: True or False?

Based on Questions tell whether True or False 1. For any normal distribution exactly 97.50% of the z-score values are less than z=1.96. 2. For any normal distribution, the proportion located between the mean and z=1.40 is 0.9192. 3. When determining the probability of selecting a score that is below the mean, you will get a

Probability of these events using basic probability principles

Suppose there are two types of Penn State Sports fans: Rabid (R), and Casual (R'). These fans either view a big game Live (L) or at Home (L'). Suppose 15% of Penn State fans are both Casual and watch the games at Home. If a fan watches at Home, the probability that he/she is Casual is 80%. Finally, suppose 10% of fans are Rabid.

Assessing Scores

Given that scores correspond with a raw score of 75.349, any individual with a raw score of 75.349 or higher would be included in your top 25%. If you have 100 scores, will this be the top 25 raw scores do you think? Why or why not?

Probability Analysis in Statistics

Find the indicated probability. 1) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 170and 220. Solve the problem 2) For women aged 18-24, sy

Probability and Roravirus

(a) A student is taking a true-false exam with 20 questions. Assuming that this student guesses at all the 20 questions. (i) Determine the probability that this students gets either fourteen or sixteen answers correct. (ii) Approximate the probability obtained in part (i) by an area under a suitable normal curve. (b) (i) U

Probabilities and Airline Bookings

When someone buys a ticket for an airline flight, there is a 90% probability that a person will not show up for the flight. Air America books 15 people on a commuter flight that can only seat 13 passengers. What percent of the time will exactly 13 passengers show on time to be seated on the flight? What percent of the time

Calculating Various Probability Problems

1. At a college, 70 percent of the students are women and 45 percent of the students receive a grade of C. About 30 percent of the students are female, but not C students. Use this contingency table. (See attached file) If a randomly selected student is male, what is the probability he is a C student? 2. The contingency tabl

Probability and Statistical Representations

A random sample of 20 people found that the number of mail-order catalogs that each had received in the last month were (in order from lowest to highest): 0 0 1 3 5 8 8 9 9 14 17 21 25 29 32 38 43 48 57 62 a) find the range, mean, median, and mode of the data set b) find the sample standard deviation. c) construct a hist

Probability: Tossing an Unfair Coin

Suppose an unfair coin comes up heads 65.2% of the time if it is flipped. If the coin is flipped 14 times, what is the probability that: a) it comes up tails exactly 6 times? b) it comes up heads more than 11 times?

Probability and Confidence Interval of Normal Distribution

The weekly incomes of a large group of middle managers are normally distributed with a mean of $1,500 and a standard deviation of $150. Use the standard normal distribution to calculate the following: 1. Find the probability that a particular weekly income selected at random is between $750 and $1,500. 2. What is the probabil

Probability of Higher Education Institutions

Public Private Total Northeast 6 14 20 Mideast 4 12 16 South 15 9 24 West 15 25 40 Total 40 60 100 The following contingency table above cross classifies institution of higher education in the United States by region and type. Suppose an institution of higher educat

Probability of a Coin Toss

A coin was flipped twenty times and landed heads fifteen times. Based upon this information, answer the following the question: If the coin is balanced (fair) what is the probability of a head on the toss? If the coin is not balanced (not fair), what is the probability of a head on the next toss? If a fair coin is flipped t

Running a Blood Bank

You are running a blood bank. Every month, a random number of hospital patients will need blood that you will supply. Also, every month, a random number of donors will come in and give blood. You goal is to provide enough blood on hand to supply those patients who need it. At the beginning of the current month you have no pin

Combined Initial Capital

In a classical ruin problem with two gamblers, the initial capital of one of the gamblers, Alice, is $90 and the combined initial capital (CIC) is $200. In each trial of the game, an unbiased coin is tossed - Alice wins when the coin shows heads. a) What is the expected duration of the game? b) Given the same CIC, how much

Probability: Acceptance Sampling

Prob 1. Acceptance sampling is a statistical method used to monitor the quality of purchased parts and components. To ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows 1 defect. a. What is the likelihood of accepting a lot that is 1% defective? b. If the quality of the inco

Return Policy and Label Weight

1) Best Electronics Inc. offers a "no hassle" returns policy. The number of items returned per day follows the normal distribution. The mean number of customers returns is 10.3 per day and the standard deviation is 2.25 per day. a. In what percent of the days are there 8 or fewer customers returning items? b. In what pe

Queuing Models

Suppose that the service rate to a waiting line system is 10 customers per hour (exponentially distributed). Analyze how the average waiting time is expected to change as the arrival rate varies from two to ten customers per hour (exponentially distributed).

Binomial Random Variables, Probability, and Normal Distribution

7.84) Given a binomial random variable with n = 10 and p = .3, use the formula to find the following probabilities. a. P(X = 3) b. P(X = 5) c. P(X = 8) 7.97) In the United States, voters who are neither Democrat nor Republican are called Independents. It is believed that 10% of all voters are Independents. A survey aske

A Discussion On Probability Distributions

6. A coin is tossed 4 times. Let X denote the number of heads which appear in 4 tosses. a) Construct a probability distribution for X b) Find P(X>2) c) Find the expected value of X d) Find the variance and standard deviation of X 7. The probability that a randomly selected elementary or secondary school teacher from a cit

The solution gives detailed discussion on definitions and calculations of specificity and sensitivity. Some further topics such as positive predictive value, negative predictive value, Lead time bias and length-bias are also explained. All formula of specificity and sensitivity are shown and explained with specific examples.

1) Sensitivity is: A. The probability that a test correctly classifies as positive those who have preclinical disease. B. The probability that a test correctly classifies individuals without preclinical disease as negative C. The probability that those who test positive have the preclinical disease D. The probability that t

Mean and Standard Deviation of Randon Variable

The random variable x with probability distribution given below X = 2 3 4 7 10 P(x) = 0.1 0.2 0.4 0.1 0.2 (a) Determine the expected value of x (b) Determine the standard deviation of x (c) Given a sample size of 65, with sample me

Probability of Outcome

A fair die is rolled two times. Let A be the event that the outcome of the first roll is an odd number. Let B be the event that the outcome of second roll is at least 5. A) What is the probability that the outcome of the second roll is at least 5, given that the first roll is an odd number? B) Are A and B independent? Why o