### Working with combinations.

I have 9 chalkboards to be distributed amongst 4 classrooms. If each class must get at least 1 chalkboard, how many possible divisions can I have?

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I have 9 chalkboards to be distributed amongst 4 classrooms. If each class must get at least 1 chalkboard, how many possible divisions can I have?

A factory employs several thousand workers, of whom 30% are Hispanic. If the 15 members of the union executive committee were chosen from the workers at random, the number of Hispanics on the committee would have the binomial distribution with n=15 and p=0.3 a)What is the probability that exactly 3 members of the committee are

If the parents have 5 children, the number who have type O blood is a random variable X that has the binomial distribution with n=5 and p=0.25 a) What are the possible values of X? b) Find the probability of each value of X. Draw a histogram to display this distribution. (Because probabilities are long-run proportions, a hi

For a given data set Mean = u=200 and standard deviation =30. What is the probability that the mean of a sample of n=36 a) would be greater than 208? b) Less than 195? c) Between 192 and 210? d) Not more than 212?

Details: An electric power trading company has an option to buy 1,000,000 terawatts of electricity from a producer for $10 per terawatt. Other electric power trading companies have received this option and the company knows a decision must be made quickly. The company estimates it can sell the electricity for $14 per terawatt if

16. If a coin is tossed three times, the likelihood of obtaining three heads in a row is a. zero b. 0.500 c. 0.875 d. 0.125 e. None of the above answers is correct. 17. If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A|B) = a. 0.05 b. 0.0325 c. 0.65 The following rep

Dollar Department Stores has received an offer from Harris Diamonds to purchase Dollar's store on Grove Street for $120,000. Dollar has determined probability estimates of the store's future profitability, based on economic outcomes, as: P($80,000) = .2, P($100,000) = .3, P($120,000) = .1, and P($140,000) = .4.

As the owner of a rent-a-car agency you have determined the following statistics: Potential Rentals Daily Probability Rental Duration Probability 0 .10 1 day .50 1 .15 2 days .30 2 .20 3 days .15 3 .30 4 days .05 4 .25 The gross profit is $40 per car per day rented. When there is demand for a c

Find the probability and expected value.

1) A $25,000 investment in a tract of land may be worth $10,000, $25,000, or $45,000 after one year, the probabilities of these values being 0.25, 0.45, and 0.3, respectively. a) What is the expected value of the investment in one year? b) If your expected return on the investment is the expected present value of the investm

1 The Kwik Klean Car Wash loses $30 on rainy days and gains $120 on days when it does not rain. If the probability of rain is 0.15, what is the expected value of net profit? 2. The Newman Construction Company bids on a job to construct a building. If the bid is won, there is a 0.7 probability of making a $175,000 profit and t

1. Compute the arithmetic mean for the following data: 8, 2.2, 25, 7, -9, 10, 2, and 5.9. 2. An Embry-Riddle senior performed the same experiment on three groups of subjects (with permission!) and obtained mean scores of 84, 69 and 76. The groups consisted of 13, 31, and 27 subjects respectively. What is the overall mea

A tire company made a sampling distribution on one of its brands of tires and determined that the tire had a mean life of 56,000 miles with a standard deviation of 18,100 miles. a. What is the probability that the life of a single tire will be less than 50,000 miles? b. What is the probability that the mean life of a sampl

2. The probability that a person is immune to a certain disease is 0.40. a) What is the probability that 4 people will have the disease in a sample of 12 people b) Find the mean number of people who have immunity in a sample size of 12. c) Find the standard deviation for the same sample 3. If the capacities of the cran

Acme Plumbing Supply has just received a shipment of 5,000 valves for chemical plants, where regular steel valves would corrode. However, it is known that in the shipment 50 of the valves are regular steel which were inadvertently included. Unfortunately there was no was to distinguish between the two types of valves. They

1)If X and Y are both discrete, show that xPX/Y9x/y)=1 for all y such that pY(y)>0. 10) Suppose X and Y are independent continuous random variables. Show that E[X/Y=y]=E[X] for all y

52) (from pg. 52) A coin, having probabiliyt p of landing heads, is flipped until head apears for the rth time. Let N denote the number of flips required. a) Calculate E[X] for the maximum random variable fo Exercise 37. b) Calculate E[X] for X as in Exercise 33. c) Calculate E[X] for X as in Exercise 34.

30)Let X be a Poisson random variable with parameter (lambda). Show that P {X=i} increases monotonically and then decreases monotonically as i increases, reaching its maximum when i is the largest integer not exceeding (lambda). Hint: Consider P{X=i}/P{X=i-1}. 37) Let X1, X2, ...., Xn be independent random variables, each

The manager of a restaurant claims that only 3% of the customers are dissatisfied with the service. If this claim is true, what is the probability that the number of dissatisfied customers, in a random sample of 25 customers will be a) 0 b) at least 1 c) between 1 and 5 inclusive d) greater than 5 e) 25

A class is given a list of 20 study problems from which 10 will be part of an upcoming exam. If a given student knows how to solve 15 of the problems, find the probablility that the student will be able to answer, a. All 10 questions on the exam b. Exactly 8 questions on the exam c. At least 9 questions on the exam

Merican air flight 2705 from N.Y. to San Francisco has seats for 340 passengers. An average of 7% of the people with reservations do not show up so American Air overbooks by accepting 355 reservations for the 340 seats. We can analyze this system by using a binomial distribution with N=355 and P=0.93 (the probability that a boo

Steps: 2) Find p-hat(R), the proportion of days on which it rained given that it rained the pervious day. 3) Find p-hat (NR) the proportion of days on which it rained given that it did not rain the previous day. 4) Construct confidence intervals for both p-hat(R) and P-Hat(NR) (you can chose level of confidence)

What is Binomial Expansion?

A researcher is studying IQ levels. From past experience she knows the population mean IQ for adults is 110 and the standard deviation is 15. a) If samples of 30 IQs are selected and the sample mean is calculated for each sample, what can be said about the sampling distribution of the sample means, and why? b) If she ta

The Bell telephone co. surveyed an apartment building with 500 units to find out who subscribes to their service. Turns out 70% of the units use Bell's service. Find the probability that less than 340 units are using Bell services so we are looking for: P(X<340) Z= 340-350/10.25=-0.98

A manager must select from among ten persons to fill four job openings. Four of the candidates belong to a minority group. If the four positions are filled at random by the candidates, what is the probability that no minority group member will be selected?

A survey of workers in the U.S. found that 2.9% work more than 70 hours per week. You randomly select 10 workers in the U.S. and ask each if he or she works more than 70 hours per week. a)find the probability that at most three people say they work more that 70 hours per week b)find the probability that at least three peopl s

A) A coin is tossed 20 times. Find probability of getting at least 14 heads. B) A die is tossed 20 times. Find probability of getting a "1" two times. C) Three dice are tossed. Find probability that a four shows on exactly two of the dice.

A wheel with the following probabilities is spun: Prob(1)= 0.50, Prob (2) = 0.20, Prob (3) = 0.30 If the wheel is spun 3 times find probability that the sum of numbers you get = 6

A new component for an airplane is being manufactured. Each has a 70% probability of working properly. A sample of 8 components is sampled. Find probability that: A) all work properly. B) 6 work properly. C) at most 3 work properly. D) at least 1 works properly.