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1. The probability density of a continuous random variable X is given a UNIFORM DISTRIBUION, U (0,2) Based on this distribution, what is the probability

1. The probability density of a continuous random variable X is given aUNIFORM DISTRIBUION,U(0,2)

Based on this distribution, what is the probability thatXis between 0.5 and 1.5? (Show Work)

2. A commuter must pass through five traffic lights on her way to work, and she will have to stop at each one that is red. Let X = the number of red lights she stops at on her way to work. She estimates the distribution for X to be as shown below:

Value of X

1

2

3

4

5

Probability

0.40

0.25

0.15

0.15

0.05

On average, how many traffic lights does the commuter expect to hit on her way to work?

(show work andyou may round answer to the tenths place)

3. A commuter must pass through five traffic lights on her way to work, and she will have to stop at each one that is red. Let X = the number of red lights she stops at on her way to work. She estimates the distribution for X to be as shown below:

Value of X

1

2

3

4

5

Probability

0.40

0.25

0.15

0.15

0.05

Calculate the SD for the number of traffic lights the commuter will hit on her way to work.

4. You paid $10 to be entered into a raffle for a prize of $1,000. If there was only going to be one winner out the total 50 people that entered, what is your expected profit for entering the raffle? (Hint, using the provided table may help) (show work to help with partial credit)

PROFIT

PROB.

5. Consider a random variable X has mean =9 and standard deviation =2. The random variable Y can be described by Y = 3X+1, compute the mean of Y.

6. Chocolate bars produced by a certain machine are labeled 8.0 oz. The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 oz and a standard deviation of 0.1 oz.

If the quality control manager takes a simple random sample of ten chocolate bars from the production line, what is the probability that the sample mean weight of the 10 sampled chocolate bars will be less than 8.0 oz?

7. Chocolate bars produced by a certain machine are labeled 8.0 oz. The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 oz and a standard deviation of 0.1 oz.

The quality control manager plans to take a simple random sample of size n from the production line. How big should n be so that the sampling distributionhas standard deviation (of x-bar)equal to 0.01 oz?

8. In the construction industry, compressive strength of concrete is a crucial characteristic. Suppose for a particular residential construction job the concrete tested should have a mean compression strength of3000 psi with a standard deviation of50 psi. It is known that compressive strength of concrete is Normally distributed. On a construction site, a sample of n = 5 specimens is selected and tested after 3 days. If the concrete has the desired characteristics, what is the probability that the sample mean will be larger than 3060 psi?

9. The chances for any adult male to have Chromosome Defect-A was published to be 0.005. A random sample of 100 adult males is selected. Let the random variable X = the number of males in the sample who have this chromosome defect.

In the space below list the reasons why X follows a binomial distribution?

10. For the following application, explain why it does not fit the binomial setting discussing all four criteria:

"An airplane has a front and rear door, both of which are opened to allow passengers to exit when the plane lands. The plane has 100 passengers aboard. Let X = the number of passengers exiting through the front door."

11. The chances for any adult male to have Chromosome Defect-A was published to be 0.005. A random sample of 100 adult males is selected. Let the random variable X = the number of males in the sample who have this chromosome defect.

Compute the probability that at most one male will have this chromosome defect. (show calculator work)

12. The chances for any adult male to have Chromosome Defect-A was published to be 0.005. A random sample of 100 adult males is selected. Let the random variable X = the number of males in the sample who have this chromosome defect.

What are the mean and standard deviation of the random variable X?

13. During the last student elections at a certain college, 45% of the students voted for the sophomore student candidate. A simple random sample of students from this college is to be selected and we can assume that the number who pick this particular candidate will follow the binomial setting.

If n=12 students are selected, what is the probability that exactly 7 of them voted for the aforementioned candidate?

14. During the last student elections at a certain college, 45% of the students voted for the sophomore student candidate. A simple random sample of students from this college is to be selected and we can assume that the number who pick this particular candidate will follow the binomial setting.

If n=120 students are selected, what is the probability that no more than 70 of them voted for the aforementioned candidate?

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