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# Probability

### Probability and Weibull Distribution

Assume the life of a rotating item follows a Weibull distribution with the shape parameter (or slope) = 2 and the scale parameter = 10,000 hours. a. Determine the probability that the rotating item lasts at least 8000 hours. b. Determine the mean time until failure of the item. c. If 10 rotating items are used in a larger com

### Explaining Probability Recurring Events

The mean time between reoccurring events is exponentially distributed with a mean time between events of 15 minutes. a. What is the probability that there are no events within a 30-minute period? Answer 0.00043 ? b. What is the probability that at least one call arrives within a 10-minute interval? Answer 0.4866 ? c. Wha

### Probability and Statistical Analysis of Products

1. At a factory, the fill volume of Coke cans is normally distributed with a mean of 12.4 fluid ounces and a standard deviation of 0.1 fluid ounce. a. What is the probability a fill volume is less than 12 fluid ounces? b. If all Coke cans less than 12.1 or greater that 12.6 ounces must be destroyed, what proportion of Coke

### Question about Probability for normal distribution

1. Find the probability that a standard normal random variable will assume a value between: a. z = 1.5 and z = .75 b. Greater than 1.25 c. Find a z such that 70% of the area is above that value. 2. In recent years, the use of the telephone as a data collection instrument for opinion polls has been steadily incr

### Statistics Problems solved in this posting are based on Poisson Distribution and Normal Distribution. For Specific Problems, please see the posted problems.

Use the Poisson Distribution to find the indicated probability. 49) For a certain type of fabric, the average number of defects in each square foot of fabric is 0.3. Find the probability that a randomly selected square foot of the fabric will contain more than one defect. 49) ______ A) 0.0369 B)

### 28) A contractor is considering a sale that promises a profit of \$ 23,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of \$ 13,000 with a probability of 0.3. What is the expected profit? 29) Choosing 3 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement, keeping track of the number of red marbles chosen. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. 33) n = 4, x = 3, p = 1/6 34) n = 10, x = 2 , p = 0.5 35) n =12, x = 5, p = 0.25 36) A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? 37) Find the probability of at least 2 girls in 10 births. Assume that male and female births are equally likely and that the births are independent events. 38) An airline estimates that 98% of people booked on their flights actually show up. If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane? Find the mean, &#956;, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. 39) n = 33; p = .2 Find the standard deviation, &#963;, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. 41) n = 36; p = .2 42) n = 2661; p = .63 43) n = 94, p = 0.20 44) n = 377, p = 2/3 45) According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16. 46) A company manufactures batteries in batches of 29 and there is a 3% rate of defects. Find the mean number of defects per batch. Determine if the outcome is unusual. 47) A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 481 consumers who recognize the Dull Computer Company name? 48) According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to "Eyewitness News" at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are randomly selected and checked to determine what is being watched. Would it be unusual to find that 872 of the 2500 televisions are tuned to "Eyewitness News"?

Solve the problem. 22) Find the variance for the given probability distribution. 22) ______ A) 2.46 B) 2.69 C) 7.43 D) 2.63 23) Find the standard deviation for the given probability distribution. 23) ______ A) 1.71 B) 1.6

### 21 prob/stats multiple choice questions

Express the indicated degree of likelihood as a probability value. 1) "You have a 50-50 chance of choosing the correct answer." 1) _______ A) 50 B) 0.50 C) 0.9 D) 0.25 2) "It will definitely turn dark tonight." 2) _______ A) 0.67 B)

### Probability of weight distribution of gerbil

The state's smallest animal is a red-tailed gerbil, with a mean weight of 2.5 grams and a standard deviation of 0.25 grams. Assuming that the weights are normally distributed, find the probability of randomly selecting a gerbil that weighs a. between 1.0 and 2.0 grams b. between 1.6 and 2.2 grams c. more than 2.2 grams

### Bayes' Theorem for Probability Revision

Set up a short problem related to your work environment to calculate the probability(ies) of an event happening. Then use Bayes' Theorem to revise the probability. Show all your work.

### Discrete & Continuous Probability Distributions

Please use Excel for this and could you send me a few notes with step by step break-down on how to make it easy to figure out next time? 1. An American Society of Investors Survey found that 30% of individuals have used a discount broker. In a random sample of 9 individuals, what is the probability That: a. Exactly 2 of t

### Find probabilities from a data set

Please answer the following probabilities from the data set below using Excel. Also please add them to the chart, Thanks. https://mycampus.aiu-online.com/courses/QMB350/Assignment_Assets/DataSetandDataSetKey_0703A.xls ? What is the gender distribution (% females and % males)? ? What is the "tenure with company" distribut

### Statistics - probability

(1) The average number of humming birds per hour on a particular feeder is 5. Find the probability that exactly 3 humming birds feed during a particular hour using the correct table or formula. (2) Weights for students applying to a Sumo wrestling school are normally distributed, with a mean of 250 pounds and a standard dev

### This posting provides solution to statistics MCQs focusing on probability, binomial probability distribution, normal probability concepts, etc

Please show all work and examples 1. Under certain conditions, it is possible that the sum of the probabilities of all the sample points in a sample space is less than one. ___ T/F 2. A compound event formed by use of the word and requires the use of the addition rule. ____ T/F 3. In any binomial probability

### Real Estate Stats Confidence Interval

Assume you have a real estate investor client who wants you to answer some specific questions about housing in the neighborhood encompassed by the 5 townships in your Real Estate Data Set. Further assume that you have collected this random sample in an effort to answer your client's questions using statistical tools.: 1. Des

### (1) Find the probability that the elevator will be overloaded if 16 people are in the elevator. (2) How many passengers would you recommend if you wanted to be sure that the overloading probability is less than 0.001?

An elevator has a design capacity of 2,560 pounds and a posted limit of 16 passengers. The weight of adults is approximately normal with a mean of 150 pounds and standard deviation of 20 pounds. Find the probability that the elevator will be overloaded if 16 people are in the elevator. How many passengers would you recommend

### Probability Calculations for JENN Inc.

JENN Inc. supplies under-hood emission control air pumps to the automative industry. The pump is vacuum-powered and works while the engine is operating., cleaning the exhaust by pumping extra oxygen into the exhaust system. If a pump fails before the vehicle in which it is installed has traveled 50,000 miles, Federal emission re

### Statistics and Process Capability : LSL, USL and CpK

Please help with the following problem. A data set contains 16 measurements as follows: 1525; 1561; 1541; 1532; 1499; 1551; 1554; 1528; 1514; 1548; 1534; 1505; 1500; 1538; 1529; 1519 the calculated mean = 1530 and the calculated std deviation = 19 The USL and LSL are respectively 1560 and 1510 and I, therefore, deri

### Probability Distribution - E-mail Potential Acquisition

E-mail Potential Acquisition You've done a great job so far, but we need you to investigate another situation. BankTen is considering an acquisition and has narrowed the possibilities to three companies. All three of these acquisitions are ongoing businesses with a profit stream and can be acquired for about the same amount o

### Probability of selling life insurance

1. The probability that a life insurance salesperson following up a magazine lead will make a sale is 30%. A salesperson has two leads on a certain day. What is the probability that the salesperson will sell: a. Both b. Exactly one policy c. at least one policy

### Continuous Probability Distribution at Hydronics Company

DATA ATTACHED The Hydronics Company is in the business of developing health supplements. Recently, the company's R&D department came up with two weight-loss plans that included products produced by Hydroniccs. To determine whether these products are effective, the company has conducted a test. A total of 300 people who eac

### Discrete and Continuous Probability Distributions

East-West Translations publishes textbooks of ancient Oriental teachings for English-speaking universities. The company currently is testing a computer-based translation service. Because Oriental symbols are difficult to translate, East-West assumes the computer program will make some errors, but then so do human translators.

### Discrete Probability Distributions Gateway 2000 Inc.

5.18 Gateway 2000, Inc., receives large shipments of microprocessors from Intel Corp. It must try to ensure that the proportion of microprocessors that are defective is small. Suppose Gateway decides to test five microprocessors out of a shipment of thousands of them. Suppose that if at least one of the microprocessors is de

### Determining the probability of surviving for 3 years using the data given

The question is based on the following information: --------------------------------------------------------------------------------- No. of Patients Alive on each anniversary Year of Treatment No. of Pati

### Introduction to Probability Distribution

A Courtyard Hotel by Marriott conducted a survey of its guests. Sixty-two surveyors were completed. Based upon the data from the survey, (see attached) determine the following: a) Two customers are selected. What is the probability that both will be on a business trip? b) What is the probability that a customer will be on

### The Rules of Probability

#1 A manager of a gasoline filling station is thinking about a promotion that she hopes will bring in more business to the full-service island. She is considering the option that when a customer requests a fill-up if the pump stops with the dollar amount at \$9.99, the customer will get the gasoline-free. Previous studies show

### Creating a Decision Tree in Excel

Management at Canron, a switch maker, is confronting a problem of determining whether or not to develop a new ultra power optical switch. The research and development costs of developing such a switch is estimated to be \$25 million. If the company goes ahead with the R&D and develops the switch, a crucial issue is whether or not

### Microprocessors Probability Statistics

1. Gateway 2000, Inc., receives large shipments of microprocessors from Intel Corp. It must try to ensure that the portion of microprocessors that are defective is small. Suppose Gateway decided to test five microprocessors out of shipment of thousands them. Suppose that if at least one of the microprocessor is defective, the

### Construct a Contingency Table

Question 1 The table below contains the opinions of a sample of 200 people (broken down by gender) about the latest congressional plan to fund abortion clinics. For Neutral Against Totals Female 38 54 12 104 Male 12 36 48 96 Totals 50 90 60 200 Find the probability that a randomly selected a)person would be

### The solution discusses the sample space and probabilities of die

Question 3 An experiment consists of rolling one die. Let A be event that the die shows more than one, B be event that the die shows more than 4, and C be event that die shows an even number. a) List the sample space of this experiment. b) Find P(A), P(B), P(C) c) Find P(A or C), P(A or B), P(A and C), P(B and C) d) A

### 8 Statistics Questions: Expected profit, probability, product demand, median life

Question 1 An investment can lead to a profit of \$10,000, \$5,000, \$4,000, and \$1,000, with respective probabilities of .4, .3, .2, and .05. In addition, there is a 3 percent chance of breaking even and a small chance of losing \$10,000. Find the expected profit. Question 2 A car dealership has combined all popular opti