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# Probability

### Complement Probability

If P(A) = .02, P(A or B)= .40 and P(AB) =0.1, what is the probability P(~B)?

### Ways to Select a Committee with Specific Gender Requirements

The school board of a public school system must select a finance committee of 5 from its 15 man, 8 woman membership. In how many ways can this committee be selected so that it consists of 3 men and 2 women?

### Binomial Distribution and NC Army National Guard

In the military, everything works of numbers. Recruiting is a good example of a binomial distribution. I'll use NC Army National Guard for an example. The NCARNG must have a set number of enlistments every year and they get the requirement for the year during October. This year the number is: 2000 (so n = 2000), the 2 ou

### Determine the portion of time the staff person is busy and how long a guest must wait for his or her request to be addressed.

The Delacroix Inn in Alexandria is a small exclusive hotel with 20 rooms. Guests can call housekeeping from 8:00 am to midnight for any of their service needs. Housekeeping keeps one person on duty during this time to respond to guest calls. Each room averages 0.7 call per day to housekeeping (Poisson Distributed), and a gues

### Binomial Probability Distribution and Probability

1. Suppose that the number of cars, X, that pass through a car wash between 4:00pm and 5:00pm on any sunny Friday has the following probability distribution: X 4 5 6 7 8 9 P(X=x) 1/12 1/12 ¼ ¼ 1/6 1/6 What is the probability that at least 7 car

### Probability and Discrete Probability Distributions Model

In paragraph form, create an example in everyday life that uses the binomial distribution as a model. Make sure that you explain how your example fits the requirements for a binomial distribution.

### Prove that no matter what the posted odds

Based on the betting model in the Two-horse race_01.xls spreadsheet, prove that no matter what the posted odds and the bets received are, the expected loss/gain is always zero. How can the bookmaker make sure he can earn a certain amount that is above the expected zero income from the betting? See attached file for ful

### Normal approximation to binomial

A multiple-choice examination consists of 90 questions, each having possible choices a, b, c, d, and e. Approximate the probability that a student will get at least 21 answers correct if she randomly guesses at each answer. (Note that, if she randomly guesses at each answer, then the probability that she gets any one answer corr

### Probability of normal distribution

A cola-dispensing machine is set to dispense on average 7.00 ounces of cola per cup. The standard deviation is 0.10 ounces. The distribution of amounts dispensed follows a normal distribution. a. What is the probability that the machine will dispense between 7.10 and 7.25 ounces of cola? b. What is the probability that t

### Statistical Process Control Help

1. A medical supplies company buys its supplies in bulk and redistributes them to doctor's offices and clinics. They receive thermometers in lots of 500 from the vendor. They are considering a sampling plan of n=50 and c=1. a. Develop a OC curve for this sampling plan. (Use Poisson Tables) b. If an incoming lot has 5% defectiv

### Automobile mileage for company's sales force

Distances driven by the sales force average 5,650 miles a month, and has a Standard Deviation of 120. Lower limit for calculation is 5,500. What percentage drove 5,500 miles or more in a month? Would like to see in Excel format to identify relevant formula.

### find the mean and standard deviation

The below table lists the last digits of the 73 published distances (in feet) of the 73 home runs hit by Barry Bonds in 2001 when he set the record for the most home runs in a season (based on data form USA today) The last digit of a data set can sometimes be used to determine whether the data have been measured or simply report

### Returned checks at a business

Issue: Returned checks at a business. 12% are returned for insufficient funds. 50% of this 12% the customer received cash back. 10% of all customers ask to receive cash back at the end of a purchase. For 1000 customer visits calculate the following: a) Insufficient funds? b) Cash back? c) Both insufficient funds an

### Probability

Express the indicated degree of likelihood as a probability value. *"it will definitely turn dark tonight." a. 0.5 b. 1 c. 0.30 d. 0.67 *Which of the following can not be a probability? a. 1 b. 0 c. -1 d. 2 *Answer the question,considering t

### Quantitative Methods: Finding Probability

Potato chip are sold in 12 oz bags. The bag weights are expected to be normally distributed about this standard. If the standard deviation of the bags is 0.58 oz would it be unusual to find a bag containing 11 oz. The Frito Lay CEO wants to know if it will be unusual for a bag to be 10% or more short.

### Quantitative Methods - Simulation to Demonstrate Probability

As you discussed earlier, four students called in to say they would miss their exam due to a flat tire. On the make-up exam the instructor as each student to list the tire that was flat. We concluded that there was only a 1/64 chance that all four would randomly agree if they actually had not had a flat. Simulate the situatio

### Quantitative Methods - should a plane go commercial probability

Management is considering going live with a new product that research believes is promising. Engineering estimates that if a \$300,000 pilot plant is build there is a 0.75 chance of a high yield versus the alternative of a low yield. If the pilot plant shows a high yield they believe there is a probability of 0.8 that the comm

### Quantitative Methods - probability of colored marbles

What is the probability of getting at most 3 white marbles when drawing 5 marbles from a bucket containing 5 white marbles and 5 black marbles?

### Determining Probability: Duration of Drug Effectiveness

Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random: a) What is the probability that the drug will be effective for 2 hours or less? b) What i

### Calculating the Probability of Occurrence

Roger has read a report that the weights of adult mail Siberian tigers have a distribution which is approximately normal with mean = 390 lb and standard deviation = 65 lb. a) Find the probability that an individual male Siberian tiger will weigh more than 450 lb. b) Find the probability that a random sample of 4 male Siberia

### Probability: Calculating Combinations

Laura is training for a week-long mountain cycling tour. She has 12 short hilly routes from which to choose mid-week rides. a) How many ways can she choose 4 different rides from the list for the first week's training if order matters? b) How many ways can she choose 4 different rides if order does not matter? c) If sh

### Variance of Poisson random variable

The number of false alarms a building fire alarm system registers has a Poisson distribution with a mean of 6 false alarms per year. The variance of the number of false alarms is what?

### Compute a probability of identical balls

An urn contains 8 balls identical in every respect except color. There are 4 blue balls, 3 red balls, and 1 white ball. a) If you draw one ball from the urn what is the probability that it is blue or white? b) If you draw two balls without replacing the first one, what is the probability that the first ball is red and the

### Waiter's Probability for Commission

John has two jobs. For daytime work at a jewelry store he is paid \$200 per month plus a commission. His monthly commission is normally distributed with a mean of \$600 and a standard deviation of \$40. At night he works as a waiter, for which his monthly income is normally distributed with a mean of \$100 and a standard deviation o

### probability a randomly selected patron

Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 70% said that they preferred beer. 60% of the patrons were male. 80% of the males preferred beer. What is the probability a randomly selected patron prefers wine is? What is the probability a randomly selected patro

### Finding probability of sample mean

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean will be between 39 and 48 minutes?

### Normal approximation to the binomial distribution

A. Tossing a Coin Simulate 6 independent tosses of a fair coin. Repeat the procedure to get 200 sets of 6 coin tosses. (That's 1200 total tosses.) List the results. Explain carefully your method of simulating the tosses, whether it involves a computer, a table of random digits, or even flipping several coins at once. Addre

### Select the best stock level.

Given Buy at \$4.00, Sell at \$7.00 Demand 0 P d .1 Demand 1 P d .2 Demand 2 p d .2 Demand 3 P d .3 Demand 4, P d .2 a.Select the best stock level. b. Repeat with salvage value of \$1

### Multiple choice questions on Probability & Hypothesis

See attached files for full problem description.

### Standard distribution

Assume that the population of heights of male college students is approximately normally distributed with mean m of 68 inches and standard deviation s of 3.75 inches. A random sample of 16 heights is obtained. d. Find the mean and standard error of the xbar distribution. e. Find P (xbar > 70) f. Find P ( xbar < 67) I kno