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John made an experiment by tossing three fair coins A++
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John made an experiment by tossing three fair coins. (Fair coin has the same probability for a tail and head ½).

(a) (5 points) List the sample space for this experiment. (All possible outcomes)

 

 

(b)(3 point) What is a probability of three tails?

 

(c) (3 points) What is a probability of exactly two tails?

 

(d) (4 points) What is a probability of at least one tail?

 

 

 

 

2.   Among UMUC students 70% own a car, 50% own a bike and 40% own both.

(a) (7 points) Draw a Venn diagram.

 

 

 

 

 

(b) (5 points) Find a probability that a randomly chosen student own a least one of the above vehicles.

 

 

(c) (5 points) What is a probability that a randomly chosen student does not own a bike?

  

 

3. A division has 12 employees, 8 males and 4 females.

(a) (5 points) In how many ways can a committee of 6 members can be selected from out of these 12?

 

 

(b) (5 points) Find the probability that a random committee contains all males?

 

 

(c) (5 points)  Suppose that the committee should have one President

which has to be a female and two ordinary members who must be males.

How many different committees are possible?

 

4. X is normally distributed with mean 12 and standard deviation 4.

(a) (5 points)Find the probability that X will be more than 10.

 

(b) (5 points) Find the probability that X will be less than 13.5

 

(c) (6 points) Find the probability that X will be between 10 and 14.5

 

(d) (7 points) Find such that P(X<a)=.85

 

(e)(7 points) Find b such that P(X> b)=.25

 

 

 

5.  (7 points)  Which of the following is not a binomial distribution and why? Justify your answer.

1. Tossing a fair quarter 10 times and looking at number of heads that shows up.

2. Rolling a fair die 10 times and looking at the number of times we get six dots showing up.

3. Rolling a fair die 10 times and keeping track of the numbers that are rolled.

4. Rolling 10 fair dice and looking at the number of dice that have 4 dots facing up.

 

 

 

 

 

6.   Among companies doing highway or bridge construction, 80% test employees for substance abuse (based on data from the Construction Financial Management Association) A study involves the random selection of 12 such companies.

(a) (3 points) Find the probability that exactly 7 of the 12 companies test for substance abuse.

 

(b) (3 points) Find the probability that at least half of the companies test for substance abuse.

 

(c) (7 points) For such group of 12 companies, find the mean and standard deviation for the number (among 12) that test for substance abuse.

 

(d) (3points) Using the results from part (c) and the range rule of thumb, indentify the range of usual value.

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