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# Probability

### Statistics

For questions 1-5 use the random variable X with values x = 2, 3, 4, 5 or 6 with P(x) = 0.05x. 1. Determine P (x = 4). a. 0.05 b. 0.10 c. 0.15 d. 0.20 2. Find P (x >= 4). a. 0.60 b. 0.45 c. 0.75 d. 0.55 3. What is P (2 < x <= 5)? a. 0.70

### Probability Problems: Random Selection

An automobile dealer sells two brands of new cars. One, C, is primarily American in original; the other, G, is primarily Japanese. The dealer performs repair work under warranty for both brands. Each warranty job is classified according to the primary problem to be fixed. If there is more is more than one problem in a given job,

### Random sample for grill owners, number of television sets

3 In a simple random sample of 1000 households, 150 households happen to own a barbecue grill. Based on the characteristics of the population, the expected number of grill owners in the sample was 180. What are the values of pie, p, and n? 4 For a population of five individuals, television ownership is as follows:

### Statistics: Probability density function, central limit theorem

See the attached file. If X1,X2,..., Xn, are (iid) , from a distribution with mean &#956; and variance &#963;^2. Define the sample mean as Xbar = (X1+X2+...+Xn) / n (a) Show that the mean and variances of the probability density function of Xbar are given as E(Xbar) = &#956; Var(Xbar) = (&#963;^2)/n b

### 9 Statistics questions: unusual sample mean, drug cure, vending machine, z scores

See attached file for questions 8 and 9. 1. The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. A- Sample of n = 75, the probability of a sample mean being greater than 229 if u = 228 and o=4.4 is (round to four

### Statistics

1. A discrete random variable can have the values x =3 x=8, or x=10, and the respective probabilities are 0.2, 0.7, and 0.1. Determine the mean, variance, and standard deviation of x. 2. According to the National Marine Manufacturers Association, 50.0% of the population of Vermont were boating participants during the m

### Statistics: Probability - Defective items in Shipment

A shipment of 10 items has two defective and eight nondefective items. In the inspection of the shipment, a sample of items will be selected and tested. if a defective item is found the shipment of 10 will be rejected. If a sample of 3 is selected what is the probability that the shipment will be rejected? Use hypergeometric

### Probability Concepts

Refer to the Real Estate data, which reports information on homes sold in the Denver, Colorado, area during the last year. a. Sort the data into a table that shows the number of homes that have a pool versus the number that don't have a pool in each of the five townships. If a home is selected at random, compute the followin

### Statistics: Probabilities, Discrete or Random Variables, Sample, Distribution and Deviation

1. Find the following probabilities: (A) Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.4 and P(A or B) = 0.65, find P(B). (B) Events A and B are defined on a common sample space. If P(A) = 0.30, P(B) = 0.50, and P(A or B) = 0.60, find P(A and B) 2. A bag of jelly belly candie

### Probability: Relative Frequencies for one-way distances

5.22 A survey of employees at a large company found the following relative frequencies for the one-way distances they had to travel to arrive at work: Number of Miles (One-Way) A B C D E F GREATER THAN AN

### Probability based on binomial distribution.

A gardner plants 12 flowers. It is perdicted that on an average, 15% of the flowers planted will die during the first winter. Using the information above, please answer the following questions: 1. What type of probability distribution is presented? 2. Find the probability that EXACTLY 5 of the flowers will die in the first

### Probability Distribution, Binomial, Random Samples, & z-scores

1. Determine whether each of the distributions given below represents a probability distribution. Justify your answer. (A) x 1 2 3 4 P(x) 1/12 5/12 1/3 1/12 (B)x 3 6 8 P(x) 2/10 .5 1/5 (C)x 20 35 40 50 P(x) 0.4 -0.2 0.5 0.3 2. Consider a binomial distribution with 14 identical trials and a probability of succe

### Expected value & Binomial probability

1. Suppose a single die is rolled once. You win \$5 if a 1 or a 3 comes up, win \$12 if a 5 comes up and lose \$10 if a 2, 4, or 6 come up. a) Complete the table that gives the expected values of each event occurring. Event x (random variable) P(x) xP(x) Rolling a 1 +5 Rolling a 2 -10 Rolling a 3 +5

### Probability: Hopelessly Romantic & Number of Passwords

1. About 8% of the populaiton are hopelessly romantic. If two people are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic? 2. A password consist of 1 letter and followed by a six diget number. How many passwords are possible if not

### Probability

I'm just taking this Statistics class and I really need help understanding how to do these problems. If you need me to increase the credits, let me know. For the following problems, determine whether a probability distribution is given. In those cases where a probability distribution is not described, identify the requiremen

### Micromedia, venture capital, widget defect, job data

13. Micromedia offers computer training seminar on a variety of topics. In the seminars each student works at a personal computer, practicing the particular activity that the instructor is presenting, Micromedia is currently planning a two -day seminar on the use of Microsoft Excel in statistical analysis. The projected fee for

### Probability of grey and blue eyes in tribe E and tribe T

> Lets say you have tribe E and tribe T. The fraction of grey eyes in tribe E is pg_e=.673 and the probability of blue eyes is pb_e = 1-pg_e=.327. Similarly for tribe T we have the fraction of grey eyes in tribe B is pg_t=.327 and the probability of blue eyes is pb_t = 1-pg_t = .673. Now with this a prior knowledge you fin

### Problem of finding which population a sample came from

The following problem has it's basis in Quantum Mechanics: Part 1) There are two tribes the Eddas, a friendly tribe, and the Thors, a hostile tribe (ignore the Aeolians and the Boreans for this part of the problem) An anthropologist has to study one or the other of these two tribes after being dropped into the area where

### Binomial Probability Distribution

Assume a binomial probability distribution has µ=0.60 and n= 200 a. What is the mean and standard deviation? b. Is this a situation in which binomial probabilities can be approximated by the normal probability distribution? Explain c. What is the probability of 100 to 110 successes? d. What is the probability of 130 or

### Statistics: observational studies, consistency, 4 rules of probability, types of events

1) Describe why observational studies are good for surveys and polls but not for showing causality 2) Define consistency as it related to standard deviation 3) List the 4 rules of probability- 4) Name the type of event probability can be applied to 5) List the 4 rules to gaming and explain why the house always wins

### Probability

Suppose that the demand for a company's product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we

### Statistics: Compare and interpret z-scores of two students; amount of cola in 12 oz can

Colleges typically use grade point average cutoffs to decide who graduates with honors and who is accepted into certain programs (such as teacher education, for example). Suppose at a particular college, a GPA of 3.0 is the cutoff for such a decision. The students in department A have a grade point average of 3.77 with a standar

### Statistics: test mean reaction time of female candidates for flight school

In a standard test for reaction time, female candidates for flight school are found to have times that are normally distributed with a mean of 0.65 seconds and a standard deviation of 0.15 seconds. If one candidate is randomly selected, find the probability that her reaction time is below the maximum allowable time of 1.00se

### Normal distributions and Z scores Box plot and relation to normal distribution Grading on a curve. Pros and Cons.

Give an example from everyday life where you could use the Normal distribution to determine the probability of something. What is a z score and how could calculating a z help you in a business situation? How does a box plot relate to the normal distribution? In what ways are they similar? In what ways are they differen

### Statistics: Poisson distribution

In the example: P(x; &#956;) = (e-&#956;) (&#956;x) / x! P(3; 2) = (2.71828-2) (23) / 3! P(3; 2) = (0.13534) (8) / 6 P(3; 2) = 0.180 Where 3! = 6, how was that number calculated? In the example: P(x < 3, 5) = P(0; 5) + P(1; 5) + P(2; 5) + P(3; 5) P(x < 3, 5) = [ (e-5)(50) / 0! ] + [ (e-5)(51) / 1! ] + [ (e-5)(52) /

### Statistics: mean, variance, standard deviation of die roll, defective bolts, blue parakeet

1) In a survey, 55% of the voters support a particular referendum. If 40 voters are chosen at random, and X is the number of voters that support this referendum, find the mean and variance of X. Place the mean in the first blank_______________ and place the variance in the second blank____________________________ 2) A die is

### Statistic Problems and Descriptive Question

I managed to do all my other questions but I cannot figure these specific problems out. They are not fully explained in the book and I cannot figure it out by searching for help online. I have worked all day yesterday and most of today on this and just cannot get these specific problems! If you could explain how to do them with

### Statistics: Find the probabilities, construct a distribution, classify as discrete or random

See attached file. 1. Find the following probabilities: (A) Events A and B are mutually exclusive events defined on a common sample space. If P (A) = 0.3 and P(A or B) = 0.40, find P(B). (B) Events A and B are defined on a common sample space. If P(A) = 0.50, P(B) = 0.50, and P(A or B) = 0.60, find P(A and B) 2. A ba

### ANOVA and Regression Calculations

Case Study of ZYX Incorporated Case Study of ZYX Incorporated Executive Summary The below details is a summary of the research and findings that was completed by Team B Enterprises. This study was conducted with the employees to determine the job satisfaction and stress level of the recently announced move to a new locat

### 2 STATS

I NEED THEM BACK WITHIN 1 HR FROM NOW.SEE DATAS CAREFULLY. 1.According to Investment Digest (&quot;Diversification and the Risk/Reward Relationship&quot;, Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 15.4%, and the standard deviation of the annual return was 24.5%; During the same