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# Probability

### Weather forecast predicts May rainfall will be three to six inches

A weather forecaster predicts that the May rainfall in a local area will be between three and six inches but has no idea where within the interval the amount will be. Let x be the amount of May rainfall in the local area, and assume that x is uniformly distributed over the interval three to six inches. a. Write the formula fo

### Statistics: Thirty percent of all customers who enter a store will make a purchase.

Thirty percent of all customers who enter a store will make a purchase. Suppose that six customers enter the store and that these customers make independent purchase decisions. (a) Let x = the number of six customers who will make a purchase. Write the binomial formula for this equation. (b) Use the binomial formula to calcu

### Decision Tree Analysis for Caribbean bank, power generator

The management of a bank in the Caribbean was concerned about the potential loss that might occur in the event of a hurricane. The bank estimated that the loss from one of these storms could be as much as \$100 million including losses due to interrupted service and customer relations. One project the bank is considering is

### 5 Statistics Problems: Normal Probability, Samples, and Confidence Intervals

1- Surveying all drug stores in the Boston area, it was found that the average cost of a chocolate mint frappe is \$30.50. The cost of a mint frappe population is normally distributed, with a standard deviation of \$0.50. If I select a drug store in the Boston area randomly, what is the probability that the cost of is chocolate mi

### Probabilities for Loan Authorization

7% of the loans authorized by the branch manager of a local bank each month will never be repaid. You will be asked to identify the probability of success (p), the mean, and the standard deviation of the loans that will not be repaid assuming 35 were authorized during the month.

### Solving puzzles; inspecting computer shipments

A multi choice exam offers 4 choices for each question. Jason guesses the answers, so he has a probability 1/4 of getting any one question correct. 1) What is the expected number of right answers Jason will get if the test has 20 questions? Data on number of puzzles solved by a person are as follows: Puzzles solved:

### Probability of randomly selected family

Select an American family randomly and count the number of people it contains. Here is the assignment of probabilities for your outcome: Number of persons: 2 3 4 5 6 7 Probability: 0.42 0.23 0.21 0.09 0.03 0.02 1) What is the probability th

### Binomial and Poisson: Baseball Fans, Favorite Cookie, Major Hurricane, and Precipitation

Work questions 1 and 2 listed below using Excel. For each question, create the entire binomial distribution for the situation described in the question. The "BINOMDIST" function will calculate the probability results. You'll need to create a binomial distribution table and distribution graph for each problem. Use the table you

### Find r and Lambda from a gamma distribution

1. Suppose that X represents diameter measurements from a gamma distribution with a mean of 3 mm and a variance of 1.5 mm^2. Find the parameters r and Lambda.

### Insured value of homes follows a certain distribution

1. An insurance company insures a large number of homes. The insured value, X, of a randomly selected home is assumed to follow a distribution with density function f(x) = 3x^-4, x > 1. Given a randomly selected is insured for at least 1.5, what is the probability that it is insured for less than 2.

### Statistics: Find Theta and Probability

1. Let X have the pdf f(x) = (3x^2)/(Theta^3), 0 < x < Theta. If P ( X > 1) = 7/8, find Theta. 2. If X has a continuous uniform distribution on the interval from 0 to 10, then find P [X+(10/X)>7]

### Probability Calculations Analysis

A TV show, DOG and CAT, recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to that show. Assume that an advertiser wants to verify that 20% share value by conducting its own survey, and a pilot survey begins with 9 households having TV sets in use at the time of a GOD and CAT broadcast: - Find

### Probability

In a region, 20% of the population has brown eyes. If 15 people are randomly selected, find the probability that at least 13 of them have brown eyes. Is it unusual to randomly select 15 people and find that at least 13 of them have brown eyes? - The probability at least 13 of 15 have brown eyes = ____ (three decimal places

### Statistics

An insurance company charges a 21 year old male a premium of \$250 for a one year \$100,000 life insurance policy. A 21 year old male has a 0.9985 probability of living for a year. From the perspective of a 21 year old male (or his estate), what are the values of the two different outcomes The value if he lives is \$_______ T

### Statistics

Based on data from a car bumper sticker study, when a car is randomly selected, the number of bumber stickers and corresponding probabilities are shown below. 0 (0.794) 1 (0.099) 2 (0.041) 3 (0.015) 4 (0.014) 5 (0.012) 6 (0.008) 7 (0.006) 8 (0.006) 9 (0.005) Does the given info describe a probability distribution

### Normally distributed output: What is true about the mean of the process?

A process when in control produces a normally distributed output with a mean of 200 and a range of 20. Ten samples of 20 each yield the following means and ranges. Sample 1 2 3 4 5 6 7 8 9 10 X-Bar 200 202 201 204 203 203 201 201 202 201 Range 19.0 20.0 20.2 20.7 19.0 21.1 19.0 20.1 20.3 21.7 Which of the following is mos

### Normal Probability: Guarantee Period of Printers

Quality control studies for Leaky Jet Computer Printers show the lifetime of the printer follows a normal distribution with a mean of 4.5 years and a standard deviation of 0.85 years. The company will replace any printer that fails during the guarantee period. How long should Leaky Jet Printers be guaranteed if the company wis

### Probability, mean, variance, standard deviation,

Please solve in Excel only. 1. The Penguin Company employs 400 men and 100 women. Of the male employees, 280 work in the plant, 40 are in the office, and 80 are field salesmen. The female employees are distributed as follows: 20 to the plant, 50 to the office, and 30 to the sales. If the CEO, Stephanie, randomly selects an

### Statistics: Probability distribution, random variable, Poisson distribution

1. Compute the following and show your steps. 3! ÷ (0!*3!) 2. Three members of a club will be selected to serve as officers. The first person selected will be president, the second person will be vice-president and the third will be secretary/treasurer. How many ways can these officers be selected if there are 30 club memb

### Probability

If a couple were planning to have three children, the sample space summarizing the gender outcomes would be: bbb,bbg,bgb,bgg,gbb,gbg,ggb,ggg: 1. Construct a similar sample space for the possible gender outcomes (using b for boy a g for girl) of two children? 2. Assuming that the outcomes listed in part 1 were equally likel

### Probability of baby girls in a test of a gender selection

In a test of a gender-selection technique, results consisted of 261 baby girls and 16 baby boys. Based on this result, what is the probability a girl born to a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?

### Exponential Probability and Confidence Interval of a Policy

At a maintenance facility the standard policy with respect to the replenishment of a particular fluid is: When the amount of fluid remaining drops to 100 litres a replenishment order is placed and during the time the replenishment is on order the demand is exponential with 1/lambda = 80 litres a. What is the probability th

### Classify as dependent or independent occurrences

Classify as dependent or independent (if two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent)? Randomly selecting a city in Texas Randomly selecting a county in Texas Is it - 2 events are independent because the occurence of one

### Bay's Theorem: Smoking Cigar

In a county, 53% of adults are male. One adult is randomly selected for a survey involving credit card usage. 1) find the prior probability that the selected person is a female? P (female) = ______ (integer or decimal) 2) It is later learned that the selected survey subject was smoking a cigar. Also, 8.7% of males smo

### What is the probability of blood type and RH factor?

Given that 2 of 211 subjects are randomly selected, complete parts 1 and 2 GROUP O A B AB Type RH+ 83 56 17 15 RH- 19 15 4 2 1) Assume that the s

### Probability

A research center poll showed 80% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief? The probability that someone does not believe that it is morally wrong to not report all income on tax returns is ____ (integer or decimal)

### Probability of getting a Republican given a female was selected

If we randomly select one politician, what is the probabilty of getting a Republican given a female was selected? Republican / Democrat / Independent Male 6 11 0 Female 68 26 3 Probability is approx = __ round to th

### Calculation of probability based on normal distribution.

The number of shark attacks per year in the US is distributed approximately normal, with a Variance of 31.8 and a standard deviation of 10. A) Determine the number of shark attacks per year that separate the top 2% from the bottom 98 % B) Determine the number of shark attacks per year that constitute the middle 80% of shar

### Stat Market Survey: Microsoft Windows as the Operating System

A survey conducted by Stat Market showed that 94% of computer users use Microsoft Windows as their operating system. Suppose 12 computers users are randomly selected. A) Find the probability that exactly 10 of them use Microsoft Windows B) Find the probability that 10 or more of them use Microsoft Windows C) Find the pr

### Analyze probability of guessing correct answers

While taking a multiple choice test, I realize I cannot answer the 5 questions without guessing. There are 5 choices for each question, A B C D or E. Only one answer is correct for each questions. What is the probability of me guessing. A) Exactly two correct B) At most two correct C) All Five Correct