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Problem category: statistics (633 problems).

Problem #31
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#1. Suppose evnts A,B, are ideedentad p(A)=1/2 9B0=1/3 P9)=1/6 find th probilities;
P(B')=

P( A intersectionB)=

P(A union c)=

#2. What is the probability that at least two people in a group of 20 have the same birthday?

#3. An honest coin is tossed 11 times. What is the probability that 11 heads in a row appear?

#4. What is the probability of obtaining at least one tail when a coin is flipped five times?


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Problem #32
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To get full credit for any answer, you must show the work you performed to get that answer. For instance, say I ask you to calculate the mean of the following set of numbers: 3,3,2. To get full credit, you must show me that you used the equation , that Sx = 3 + 3 + 2 = 3 and n = 3, so the answer is . Show your answers to three decimal places.


1. Your firm has been commissioned to do a study for the local health department on the birth weight of newborn babies. One of your colleagues suggests that birth weight is related in some way to birth order (whether the baby is his motherís first, second, third, etc.). Your boss gives you the birth order of the following babies selected at random from Local General Hospital and asks you to perform some preliminary calculations:

1,3,2,1,4,1,2,1,3,1,2,1


Given this data, calculate the mean birth order of all babies born at Local General.

a. What equation do you use to calculate the mean?
b. Show all work.
c. What is the mean, to three decimal places of accuracy?


2. Given the same data, calculate the median and mode birth order.

a. Describe the method you use to calculate the median?
b. What is the median, to three decimal places of accuracy?
c. What is the mode?


3. Given the same data, calculate the variance of the birth order of all babies born at Local General.

a. What equation do you use to calculate the variance?
b. Show all work.
c. What is the variance, to three decimal places of accuracy?


4. Given the same data, calculate the standard deviation of the birth order of these twelve babies only.

a. What equation do you use to calculate the standard deviation?
b. Show all work.
c. What is the standard deviation, to three decimal places of accuracy?

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Problem #33
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Problem text:

1. Your firm has been commissioned to do a study for the local health department on the birth weight of newborn babies. One of your colleagues suggests that birth weight is related in some way to birth order (whether the baby is his motherís first, second, third, etc.). Your boss gives you the birth order of the following babies selected at random from Local General Hospital and asks you to perform some preliminary calculations:

1,3,2,1,4,1,2,1,3,1,2,1


Given this data, calculate the mean birth order of all babies born at Local General.

a. What equation do you use to calculate the mean?
b. Show all work.
c. What is the mean, to three decimal places of accuracy?


2. Given the same data, calculate the median and mode birth order.

a. Describe the method you use to calculate the median?
b. What is the median, to three decimal places of accuracy?
c. What is the mode?


3. Given the same data, calculate the variance of the birth order of all babies born at Local General.

a. What equation do you use to calculate the variance?
b. Show all work.
c. What is the variance, to three decimal places of accuracy?


4. Given the same data, calculate the standard deviation of the birth order of these twelve babies only.

a. What equation do you use to calculate the standard deviation?
b. Show all work.
c. What is the standard deviation, to three decimal places of accuracy?

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Problem #34
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Dr. Stallter has been teaching basic statistics for many years. She knows that 80 percent of the students will complete the assigned problems. She has also determined that among those who do their assignments, 90 percent will pass the course. Among those students who do not do their homework, 60 percent will pass. Mike Fishbaugh took statistics last semester from Dr. Stallter and received a passing grade. What is the probability that he completed the assignments?

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Problem #35
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Three Intro to Stat Questions.

1. Jung, a professor of psychology at the University believes that students no longer take an avg. of 22 minutes to complete a standard essay question on an exam. To test this belief, Jung selects a random sample of 64 students. Assume the standard deviation of the time to complete the essay question is known to equal 8 minutes.
Calculate the standard error of the mean. If the calculated value of the associated test statistic equals ?, what is the mean time to complete the essay question for the students in the sample?

2. A random sample of ten 1-bedroom apts in the college park, md area revealed the following rents per month (in dollars): 700, 850, 800, 705, 650, 750, 715, 695, 850, 595

Do the sample data support the belief (okay, hypothesis) that the mean rent of all 1-bedroom apts in college park area is greater than 700 per month? State the relevant hypotheses, the calculated test statistic, your decision, and your conclusion (use alpha = 0.10)

3. Consider the following hypothesis test: Null Hypothesis mu=50 Alternative Hypothesis: mu not = 50

Assume a random sample of 23 cases or observations: Determine the p-value for each of the following values of the calculated test statistic and state your decision about the null hypothesis in each case (use alpha = .05):

a. t=1.717
b. t=2.508
c. t=1.321
d. t=2.291
e. t=1.5165

I just need the answers with little relevant work.

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Problem #36
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Scores on a 100 questtion test have disribution approximated by the function

P(s)=(s-60)^2(s-90)^2 divided by 8100, 60 <= s <= 90,

where P is the percentage of people who answer s questions correctly. Find the most common score by graphing the function.

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Problem #37
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Forty-nine items are randomly selected from a population of 500 items. The sample mean is 40
and the sample standard deviation 9. Develop a 99 percent confidence interval for the population
mean.

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Problem #38
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Schadek Silkscreen Printing, Inc. purchases plastic cups on which to
print logos for sporting events, proms, birthdays, and other special occasions. Zack Schadek, the owner, received a large
shipment this morning. To ensure the quality of the shipment, he
selected a random sample of 300 cups. He found 15 to be defective.

a. What is the estimated proportion defective in the population?
b. Develop a 95 percent confidence interval for the proportion
defective.
c. Zack has an agreement with his supplier that he is to return lots
that are 10 percent or more
defective. Should he return this lot? Explain your decision

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Problem #39
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The mean rent for a one-bedroom apartment in Southern California is
$1,200 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 50 one-bedroom apartments and finding the mean to be at least $950 per month? The standard deviation of the sample is $250.

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although the population is not normal distribution, since the sample size is 50, (bigger than 30), so by hte law of large number theorem, we can still assume that the sample obey the normal distribution. then,
Let m be the mean of sample
P(m>950)
= P((m-1200)/(250/sqrt(50))>(950-1200)/(250/sqrt(50)))
=P((m-1200)/(250/sqrt(50))>-7.07)
= Z(x>-7.07)
=1

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Problem #40
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There are five sales representatives at Mid-Motors Ford. The five
representatives and the number of cars they sold last week are:

Sales Cars
Representative Sold

Peter Hankish 8
Connie Stallter 6
Ron Eaton 4
Ted Barnes 10
Peggy Harmon 6

a. How many different samples of size 2 are possible?
b. List all possible samples of size 2, and compute the mean of each
sample.
c. Compare the mean of the sampling distribution of the sample mean
with that of the population.
d. On a chart similar to Exhibit 4Ė42, compare the dispersion in the
sample mean with that of the population.

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633 problems on 64 pages.
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