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Probability

Conditional Probabilities and Malaria

A medical test for malaria is subject to some error. Given a person who has malaria, the probability that the test will fail to reveal the malaria is 0.06. Given a person who does not have malaria, the test will correctly identify that the person does not have malaria with probability 0.91. In a particular area, 20% of the

Probability and Statistics Questions

1. A large shipment of computer chips is known to contain 8% defective chips. Suppose you select 500 chips at random. (a) What distribution does the number of defective chips in the sample of 500 satisfy? (Please characterize its relevant parameters.) (b) Suppose that you wish to calculate the probability that the numb

Expected Number of Lives Saved by the Defibrillator

Suppose that over the next several years, there will be 100 cardiac incidents at Silver's. Without a defibrillator, 30 victims will die before paramedics arrive. With a defibrillator, there is an 80% probability of saving a victim who would die without it. However, there is a 3% probability that improper use of the defibrilla

Confidence Interval & Hypothesis Testing: Cure Rate

A standard surgery was performed on 50 patients with severe sinus infection, and 36 were cured. a) Find a 95% confidence interval for the population cure rate or proportion. =0.5955, 0.8445 b) Do these data indicate that the population cure rate or proportion is more than 70%? Do a hypothesis test. Use alpha=0.05. z=0.30

Normal Probabilities with Z-Score

I need some help figuring this question out: Let x be a random variable that represents the speed of the first vehicle passing an observation point between 11am to 12n on a remote highway, automatically recorded by a police radar. Based on past recording over many days, the random variable has an approximate normal distributio

Conditional Probability and Fisher's Exact Test

I need some help answering this conditional probability question: The following table is based on a random sample of 100 employee in a large fortune 500 company # of days a week one exercises 2 or fewer days 18 (Male) 12 (Female) 3 or more d

Probability Questions

Looking for assistance to make sure I am calculation answers correctly for the following 2 scenarios. Please provide the answer and any formulas in excel spreadsheet. A standard deck of playing cards consists of fifty-two cards. The cards in each deck consist of four suits, namely spades (♠), clubs (♣), diamonds (♦)

Calculation of Normal and Binomial Probabilites

Question 1: A railway company operates a number of different services. One of these connects two cities and the journey time is assumed to be normally distributed with a mean of 125 minutes and a standard deviation of 5 minutes. The company operates a scheme where it refunds 25% of the fare paid if the journey takes longer t

Ethical issues on advertising the lottery

Do you think the state has any intention of ever stopping the lottery, given the fact that the state relies on it to bring millions of dollars into its treasury? Is it possible that lottery can make everyone a millionaire? Is it ethical to suggest that the purpose of the lottery is to make everyone a millionaire? FORMAT I. I

Events Relations in Statistics

1. According to an Ipsos poll, the perception of unfairness in the U.S. tax code is spread fairly evenly across income groups, age groups, and education levels. In an April 2006 survey of 1,005 adults, Ipsos reported that almost 60% of all people said the code is unfair, whereas slightly more than 60% of those making more than $

Z scores, Z statistics, p-value and APA format

Given the research scenario, data points, set of population parameters and alpha set at p = .05, generate the correct: - Pair of hypotheses for each data point - A z statistic and p value for each data point - Decision about the null hypothesis for each data point - APA-formatted statement of results for each data point

Probability for population proportion

In an online survey of 4,001 respondents, 8% were classified as productivity enhancers who are comfortable with technology and use the Internet for its practical value (data extracted from M. Himowitz, "How to Tell What Kind of Tech User You Are," Newsday, May 27, 2007, p F6). Suppose you select a sample of 400 students at your

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

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.

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 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

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

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