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# Probability

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### Probability of a Type II Error

Calculate the probability of a Type II error for the following test of hypothesis, given that µ = 203 H0 = µ = 200 H1 = µ != 200 significance = .05 standard deviation = 10 n= 100

### Distribution of the difference of two sample means.

Suppose that we have two normal populations with the means and standard deviations listed here. If random samples of size 25 are drawn from each population, what is the probability that the mean of sample 1 is greater than the mean of sample 2? Population 1: mean = 40 and SD = 6 Population 2: mean = 38 and SD = 8

### The manager of a restaurant believes that waiters and waitresses who introduce themselves by telling customers their names will get larger tips than those who don't. In fact, she claims that the average tip for the former group is 18%, whereas that of the later is 15%. If tips are normally distributed with a standard deviation of 3%, what is the probability that in a random sample of 10 tips recorded from waiters and waitresses who introduce themselves and 10 tips from those who don't, the mean of the former will exceed that of the latter?

The manager of a restaurant believes that waiters and waitresses who introduce themselves by telling customers their names will get larger tips than those who don't. In fact, she claims that the average tip for the former group is 18%, whereas that of the later is 15%. If tips are normally distributed with a standard deviation

### Probability - Red Lobster restaurant regularly surveys customers

The red lobster restaurant chain regularly surveys its customers. On the basis of these surveys, the management of the chain claims that 75% of its customers rate the food as excellent. A consumer testing service wants to examine the claim by asking 460 customers to rate the food. What is the probability that less than 70% ra

### The restaurant in a large commercial building provides coffee for the building's occupants. The restaurateur has determined that the mean number of cups of coffee consumed in a day by all the occupants is 2.0 with a standard deviation of .6. A new tenant of the building intends to have a total of 125 new employees. What is the probability that the new employees will consume more than 240 cups per day?

The restaurant in a large commercial building provides coffee for the building's occupants. The restaurateur has determined that the mean number of cups of coffee consumed in a day by all the occupants is 2.0 with a standard deviation of .6. A new tenant of the building intends to have a total of 125 new employees. What is the

### The heights of north American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches.

The heights of north American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches. a) What is the probability that a randomly selected woman is taller than 66 inches? b) A random sample of four women is selected. What is the probability that the sample mean height is greater than 66

### Probability: Solving Statistics Problems

The question file is attached.

### Assume the probability of the birth of a boy is 0.5.

Assume the probability of the birth of a boy is 0.5. ... [See the attached question fle.]

### Probability Using Binomial Distribution

A recent survey indicated that 82% of single women aged 25 years old will be married in their lifetime. Using binomial distribution find the probability that 2 or 3 women in a sample of 20 will never be married.

### Probability: Sales Calls Will Result in an Order

An industrial chemical to retard the spread of fire in paint has been developed. From past experience, 48% of sales calls will result in an order. a) What is the probability that the first order will come on the fourth sales calls of the day? b) If eight sales calls are mad in a day, what is the probability of receiving ex

### Probability - A production process manufacturers alternators. On the average, 1% of the alternators will not perform properly when tested in the plant. When a large shipment of alternators is received at the plant, 100 are tested, and, if more that 2 are defective, the shipment is returned to the manufacturer. What is the probability of returning a shipment?

A production process manufacturers alternators. On the average, 1% of the alternators will not perform properly when tested in the plant. When a large shipment of alternators is received at the plant, 100 are tested, and, if more that 2 are defective, the shipment is returned to the manufacturer. What is the probability of retur

### Probability of Employees in the Sample Working at the Plant

Axline Computers manufactures personal computers at 2 plants. The Texas plant has 40 employees, the Hawaii plant has 20. A random sample of 10 employees is to be asked to fill out benefit questionnaires. A. What is the probability that none of the employees in the sample work at the plant in Hawaii? B. What is the probab

### According to a survey of American households, the probability that the residents own 2 cars if annual household income is over \$25,000 is 80%. ...

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over \$25,000 is 80%. Of the households surveyed, 60% had incomes over \$25,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income over \$35,000 a year is. a.

### Probability - Solving Statistics

A study found that on a given day 76% of women and 46% of men made their beds. in the U.S. women comprise 51% of adults. Find the following: a) the percentage of all adults who are men and made their beds. b) the percentage of all adults who are women and made their beds c) the percentage of all adults who make their beds

### Probability: Random Variables

A random variable has probability density function defined by f(x) = k x / ( 5x^2 + 1 )^(3/2) on the interval [ 0 , sqrt(3) ]. Find the value of k and then the probability that sqrt (8/5) &#8804; x &#8804; sqrt(3).

### Research Design, Probability, Discrete/Continuous Distributions

1. A small business owner is experiencing a high staff turnover and wants to design a study to investigate the problem. Please identify following elements of this research study. a. Research problem b. Research design c. Hypothesis to be tested d. Data collection methods e. Unit of analysis. 2. Sara scored 75 in a sta

### Comparing z-scores and probability

Please see the attached file. 1. An article in USA Today stated that "Internal surveys paid for by directory assistance providers show that even the most accurate companies give out wrong numbers 15% of the time." Assume that you are testing such a provider by making 10 requests and also assume that the provider gives the wro

### Joe Kelly's oil change and tune-up place :Simulation

3. The number of cars arriving at Joe Kelly's oil change and tune-up place during the last 200 hours of operation is observed to be the following: # of Cars Frequency 3 0 4 10 5 30 6 70 7 50 8 40 9

### An operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers.

2. The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. # of Workers Low Compliance Medium Compliance High Compliance 1 50 50 50 2 100 60 20 3 150 70 -10 a. If he

### Probability Distribution, Expected value and Variance

A player rolls two dice. The player receives \$1 for each dot on the face of two dice. For example, he will be paid \$9 if the face of the dice show a 4 and a five. let X= the number of dollars won each game. a) is X a discrete or continuous random variable? b) Show the probability distribution of X. c) Find the expected val

### Probability and Normal Distribution

A packaging company distributes quarter-pound beef patties to local fast-food restaurants. The restaurants demand the weights to be 4 plus or minus .02 ounces. If the patties are too small the customers will complain, if there will be too few of them in each box and the company will loose money. if the standard deviation of the

### Probability and Tree Diagrams

A craftsperson makes stuffed animals for sale. 85% of the animals she makes are bears while the remaining 15% are rabbits. Suppose she sells 75% of her bears at craft shows but only 50% of her rabbits are sold at craft shows. What proportion of her animals does she sell at craft shows? Make a tree Diagram.

### Exercise 5. One die is rolled. Find the probability of rolling a two given that an even number has been rolled. ...

Exercise 5. One die is rolled. Find the probability of rolling a two given that an even number has been rolled. Exercise 6. In a small, rural town in Pennsylvania, 62% of the work force is classified as "blue collar". It is also known that 72% of the blue collar workers are dog owners and that 56% of the white collar w

### Probability and Statistics - Flying Approximately

1 Flying approximately 40 billion passenger -miles per month , US airlines average a bout 4 fatalities per month . Assume that probability distribution for X , the number of fatalities per month , can be approximated by a Poisson probability distribution . What is the probability that more than two fatalities will occur in Sept

### Probability of Tossing a Coin

A coin is tossed repeatedly until a H shows up. What is the probability that (1) H shows up for the first time on the eighth toss? (2) H shows up for the first time before the 10 th toss?

### Binomial Probability of Snow Storms

4a. If the probability of a snow storm producing over 20 inches of snow in Easton, PA in a given winter is .33, what is the probabilty that over a period of 10 winters-they will have had 2 winters with such a storm? (Note-by using the binomial distribution for this problem, we're assuming that a success is a winter with a snowst

### Four cards on each of which is marked off side 1 and side 2

Consider four cards on each of which is marked off side 1 and side 2 ... [Please see the question file for full description of the problem.]

### Probability

A) In a (poorly run) widget factory, it is known that 25% of all products off the line will be defective. A random sample of 5 widgets is taken on a certain day. What is the probability that all of the widgets are defective? What is the probability that none are defective? B) A coin is flipped 5 times in a row. What is t

### Probability - Managerial Decision Making Functions

Managerial decision making Chapter 5#18 Let P(X) =.55 and P(Y) =.35 Assume the probability that they both occur is .20 What is the probability of either X or Y occurring? [See the attached question file.]

### Statistics - Probability - Runzheimer International, a management consulting firm specializing in transportation reimbursement, released the results of a survey on July 28, 2005. It indicated that it costs more to won a car in Detroit, an amazing \$11,844 a year for a mid-sized sedan, ... [See the attached question file.]

Runzheimer International, a management consulting firm specializing in transportation reimbursement, released the results of a survey on July 28, 2005. It indicated that it costs more to won a car in Detroit, an amazing \$11,844 a year for a mid-sized sedan, than in any other city in the country. The survey revealed that insuranc