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**Vandalize****Member**- Registered: 2012-12-11
- Posts: 4

1. Based on data from Carmax.com, when a car is randomly selected the number of bumper stickers and the corresponding probabilities are: 0(0.824); 1(0.083); 2(0.039); 3(0.014); 4(0.273); 5(0.008); 6(0.008); 7(0.004); 8(0.004); 9(0.009)

a. Does the given information describe a probability distribution?

b. Assuming that a probability distribution is described, find its mean and standard deviation

c. Use the range rule of thumb to identify the range of values for usual numbers of bumper stickers

d. It is unusual for a car to have more than one bumper sticker? Explain.

2. The midterm exam in a nursing course consists of 75 true/false multiple choice questions. Assume that an unprepared student makes random guesses for each of the answers. Let the random variable X be the number of correct answers in the Exam.

a. Explain why X is binomial random variable. (Find n,p,q)

b. Find the mean and the standard deviation for the number of correct answers of each student

c. What is the Probability of having at most one correct answers?

d. Would it be unusual for a student to pass this exam by guessing and getting at least 45 correct answers? Why or why not?

3. Assume that weights of men are normally distributed with a mean of 172 lb. and standard deviation of 29 lb.

a. Find the probability that if an individual man is randomly selected, his weight will be greater than 180 lb.

b. Find the probability that 20 randomly selected men will have a mean weight that is greater than 180 lb.

c. If 20 men have a mean weight greater than 180 lb, the total weight exceeds the 3500 lb safe capacity of a particular water taxi. Based on the preceding results, is this a safety concern? Why or why not?

When you solve it, Can you explain the steps? I am having trouble with these questions. Thanks

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

Welcome to the forum.

Explain why X is binomial random variable.

Two choices, true or false.

2)

b

The mean is np, the standard deviation is √(npq)

c

d)

The probability of getting 45 or more right by guessing.

I would need to know your confidence interval to determine whether that is unusual or not.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Vandalize****Member**- Registered: 2012-12-11
- Posts: 4

Thanks, My paper didn't give me confidence interval

*Last edited by Vandalize (2012-12-11 04:56:01)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

3 a)

b) I am getting

c) There is almost an 11% chance that the mean of the 20 guys exceeds 3600 lbs, so I would say yes.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Vandalize****Member**- Registered: 2012-12-11
- Posts: 4

Can you explain how you got the answer for c and d on question 2?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

I used the discrete binomial distribution which gives an exact answer here. You could use the Normal distribution which would give an approximate answer.

2c

2d

This was done by computing this sum which gets the exact answer:

Or you can use the Normal distribution to approximate the binomial.

which is close to the exact answer.

1) a

Do those numbers add up to 1? If they do we have a probability distribution.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Vandalize****Member**- Registered: 2012-12-11
- Posts: 4

Thanks

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi;

For 1b;

Assuming that a probability distribution is described, find its mean and standard deviation.

You should know how to get a mean and a standard deviation with a table of data.

I need some sleep, see you later.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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