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# Probability

### Normal distribution and stock

You're not sure if you should buy a stock and need to discover the probability of the stock having a positive return (based on one year). The annual rates are: mean=4% & standard deviation = 5%

### Jim is considering pursuing an MS in Information Systems degree. Normal distribution problems.

Problem 3 Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will be accepted at one and only one university? Problem 5 T

### Standard Normal Variables

Let z be a standard normal random variable and calculate the following probabilities: p (0.72is less than z which is less than 2.17) p (z is greater than -2) = p(z is less than or equal to -1.8

### The amount of time ships spend at the Philadelphia dockyard follows an exponential distribution and the average time spent in the dockyard is 3.1 days.

Problem 1 The amount of time ships spend at the Philadelphia dockyard follows an exponential distribution and the average time spent in the dockyard is 3.1 days. a. What is the probability that a randomly selected ship spends no more than 1.5 days at the dockyard? b. What is the probability that a randomly selected ship spend

### A standardized test consists entirely of multiple-choice questions, each with 5 possible choices.

A standardized test consists entirely of multiple-choice questions, each with 5 possible choices. You want to ensure that a student who randomly guesses on each question will obtain an expected score of zero. How would you accomplish this?

### Probability of Magazine Subscription

Several Students enrolled in a finance course subscribe to Money magazine. If two students are selected at random from this class, the probability that neither of the chosen students subscribes to Money is 0.81. Furthermore, the probability of selecting one student who subscribes and one student who does not subscribe to this ma

### Wages in Construction Industry

Wages in the construction industry average \$11.90 per hour with a standard deviation of \$1.40. What percent of workers make less than \$10.50 per hour (z = -1.00)? 2. The probability of employees taking the time to fill out a survey at Comptex is 17%. There are 5 people in the department managed by Alice. What is

### Lognormal Distribution & Probability

1. If X, Y are lognormal distribution, what the distribution of X/Y? 2. what is the probability of getting 40 or less heads in 100 coin tosses. What distribution is this. With what other distribution can you approximate this. What is the final probability. 3. Which is greater exp((a+b)/2) or (exp(a)+exp(b))/2 4. what

### Average IQ Probability

Assume that adults have a normally distributed IQ scores with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected adult has an IQ less than 135. P(IQ < 135) =

Your store wraps gifts 2 hour after they are recieved. The distribution of times is approximately normal, the standard deviation is 15 mins, today you wrapped 120 gifts (Empirical rule). a. how many gifts would expect to wrap within 2 hours 15 mins of being received. b. how many gifts would you expect to be wrapped within 1

### A hosptial has 500 patients - I sample 100 regarding opinion on quality of care - 74 are favorable.

A hosptial has 500 patients - I sample 100 regarding opinion on quality of care - 74 are favorable. Data is assumed to be normally distributed. Use this sample to predict the population proportional and to do so with 98% confidence- (finite correct factor). a. what is the lower limit for this 98% confidence interval b. what i

### Let X be a random variable representing the sum of trials.

Let X be a random variable representing the sum of trials. Then X is a binomial random variable if all of the following are satisfied except a. no two trials can have the same outcome b. p, the probability of "success" on any trial is the same for all trials c. each trial has exactly two possible outcome

### Complement Events

If event B is the complement of event A , then?

### Probability of Smokers

For questions 1 through 3 use the table below. The table shows the number of smokers and nonsmokers by gender among 220 people. Assume one person is chosen at random from the 220. Smokers Nonsmokers Totals Male 40 60 100 Female 40 80 120 Totals 80 140 220 1. If a smoker is chose

### Probability of Cracked Eggs

A carton contains 12 eggs, five of which are cracked and seven of which are good. If four eggs are chosen at random, what is the probability that there will be three cracked and one good among the four chosen?

### Popularity of Presidential Candidates

Nine presidential candidates are ranked in popularity according to a recent poll and the top three in order are announced: George (1); Thomas (2); and James (3). If three candidates were picked at random, what is the probability of picking those three and in that order?

### In establishing warranties

In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standa

### Determining the probability of S1

States A1 A2 A3 1 12 -2 8 2 4 10 5 Where; S1 is State of Nature 1, A1 is Action Alternative 1 S2 is State of Nature 2, A2 is Action Alternative 2 A3 is Actio

### The following payoff matrix is given in dollars

The following payoff matrix is given in dollars: EVENT PROBABILITY ACTION A ACTION B 1 0.5 400 700 2 0.5 200 500 The coeffici

### What is the optimal action using the EMV criterion?

EVENT PROBABILITY ACTION A ACTION B 1 0.5 400 700 2 0.5 200 500 Referring to the table above, what is the optimal action using the EMV criterion? ACTION A ACTION B EITHER ACTION A OR B IT CANNO

### Tree Diagrams for Conditional Probabilities

Please see attached file for full problem description. Tree diagrams for conditional probabilities A course in statistics is one of the most difficult at the local university. Because of this, for the past decade the university has arranged for teaching assistants to hold frequent discussion sessions as part of the course.

### probability of selecting gloves randomly

A box of 9 gloves contains two left handed gloves and seven right handed gloves. a: If two gloves are randomly selected from the box, without replacement, what is the probability that both gloves will be right handed? b: If two gloves are randomly selected from the box without replacement, what is the probability that ther

### Probability calculation for normal distribution ..

1. The average salary for graduates entering the actuarial field is \$40,000. If the salaries are normally distributed with a standard deviation of \$5,000, find the probability that a) An individual graduate will have a salary over \$45,000. b) A group of nine graduates will have a group average over \$45,000. 2. The natio

### Calculation of probability based on sampling distribution is discussed in the answer.

Replacement times for new Ford Taurus GL automobiles are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years. Find the probability that seven randomly selected Taurus GL automobiles will have a mean replacement time greater than 7.0 years. Among U.S. households, 24% have telephone answer

### Probability of Trip Duration

The time it takes to travel from home to the office is normally distributed with: (mean) = 25 minutes and (standard deviation) = 5 minutes. What is the probability the trip takes more than 40 minutes?

### Probability of Gas Mileage

The average gas mileage of a certain model car is 30 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 2.1, What is the probability that a car has a gas mileage of between 29.8 and 30.6 miles per gallon?

### What is the probability that a tree is less than 13 feet tall?

The average height of flowering cherry trees in a nursery is 11 feet. The heights are normally distributed with a standard deviation of 1.6, What is the probability that a tree is less than 13 feet tall?

### Probability Determination of Standard Normal Distribution

What is the probability P(0.36 < z < 1.43) using the standard normal distribution?

### Normally Distributed Age of Doctors

The average age of doctors in a certain hospital is 43.0 years old with a standard deviation of 8.0 years. If 25 doctors are chosen at random for a committee, what is the probability that the mean age of those doctors is less than 43.96 years. The variable is normally distributed. Need the probability that the mean age of the