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Probability and normal distribution

1. MCQ: The first test in Introductory Algebra had a mean of 82 with a standard deviation of 15. If a student made a 94 on the test, what is the corresponding z-score?
a) -0.58 b) -0.47 c) 0.47 d) 0.80 e) NOT

2. Students are sorted according to sex (male, female), grade level (lower division, upper division, and graduate student), and hair color (blond, brunette, redhead). Using a tree diagram, how many different classifications are possible?
a) 8 b) 12 c) 18 d) 24 e) NOT

3. MCQ: In a class of 22 students, there are 15 males and 7 females. If a committee of three is randomly selected, what is the probability that two are females and one is a male?
a) 3/44 b) 4/55 c) 21/44 d) 9/44 e) NOT

4. MCQ: In a shipment of 30 television sets, 3 are defective. If two sets are randomly selected and tested, what is the probability that neither set is defective? The first one is not replaced before the second one is selected.
a) 1/145 b) 117/145 c) 2/3 d) 3/290 e) NOT

5. TFQ: The number of people in a restaurant at noon is an example of a continuous variable.

6. TFQ: The time it takes to fill your car's gas tank is an example of a continuous variable.

7. TFQ: Using the probability distribution shown below, the mean would be 1.3 .
x | 0 | 1 | 2 | 3
P(x)| 0.4 | 0.3 | 0.1 | 0.2

8. TFQ: If a coin is tossed 4 times, the probability of getting exactly 2 tails would be 1/2 .

9. TFQ: The probability of getting a defective light bulb is 0.002. Then in a shipment of 3000 light bulbs we would expect to get 6 defective ones.

10. MCQ: If a gambler rolls two dice and gets a sum of 8, she wins $15, and if she gets a sum of 11, she wins $20. The cost to play the game is $5. What is the expectation of this game?
a) -$3.06 b) -$2.78 c) $2.22 d) -$1.81 e) NOT

11. MCQ: A box contains ten $1 bills, four $5 bills, and six $10 bills. A person is charged $5 to reach into the box and randomly select a bill. What is the expected value of this?
a) -$1 b) $1 c) -$2 d) -$0.50 e) NOT

12. MCQ: Using the binomial formula, if n = 8 and p = 0.68, what is the probability of getting exactly four successes, correct to three decimal places?
a) 0.324 b) 0.145 c) 0.157 d) 0.186 e) NOT

13. MCQ: A cancer center in Wisconsin conducted research on women who breastfed their babies for a year or longer and found that 30% of them had a reduced risk of breast cancer. If 20 women who breastfed their babies for a year or longer are selected at random, what is the probability that 7 or fewer would have a reduced risk of breast cancer? Do not use the normal approximation to the binomial distribution on this one. If your answer is within a thousandth or two of one of the question answers, do not choose NOT.
a) 0.113 b) 0.772 c) 0.227 d) 0.180 e) NOT

14. MCQ: A student randomly guesses at each of 8 multiple choice questions. Each question has 5 possible choices. What is the probability that the student gets exactly 4 correct?
a) 0.115 b) 0.227 c) 0.046 d) 0.124 e) NOT

15. MCQ: Nine people apply for a job as a bank teller. Four have completed college and five have not. If the manager selects three applicants at random, what is the probability that all of the three have completed college?
a) 5/42 b) 1/21 c) 11/84 d) 5/84 e) NOT

16. TFQ: In a normal curve graph, the mean divides the area under the bell-shaped curve into two equal halves.

17. TFQ: The area under the normal curve that lies within three standard deviations of the mean is about 99.7%.

18. TFQ: The area under the normal curve between z = 0 and z = 1.15 is 0.3749 .

19. TFQ: The area to the left of z = 2.83 under the normal curve is 0.9977 .

20. TFQ: The area to the left of z = 0.47 under the normal curve is 0.3192 .

21. MCQ: The average number of days a person will be sick this year is 8 with a standard deviation of 3. The distribution is normal. If a person is picked at random, the probability that she or he will be sick less than 6 days would be
a) 0.1584 b) 0.2487 c) 0.3452 d) 0.3516 e) NOT

22. MCQ: What is the area under the normal distribution curve between z = -1.43 and z = 0 ?
a) 0.0764 b) 0.4236 c) 0.5764 d) 0.9236 e) NOT

23. MCQ: What is the area under the normal distribution curve to the left of z = -1.84 ?
a) 0.0329 b) 0.1372 c) 0.4671 d) 0.9671 e) NOT

24. MCQ: Using the standard normal distribution, what is P(z <-2.09)?
a) 0.4817 b) 0.0183 c) 0.0019 d) 0.5183 e) NOT

25. MCQ: What is the z-value to the left of the mean where 59.18% of the normal distribution lies to the right of it?
a) z = 0.23 b) z = 1.33 c) z = -0.23 d) z = 0.24 e) z = NOT

26. MCQ: What z-value corresponds to the 22nd percentile in a normal distribution?
a) z = 0.77 b) z = -0.58 c) z = -0.63 d) z = -0.77 e) z = NOT

27. MCQ: The average hourly wage of workers in a fast food restaurant is $5.85 with a standard deviation of $0.35. Assume that the distribution is normal. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns less than $5.50 an hour?
a) 0.0271 b) 0.1026 c) 0.1587 d) 0.2369 e) NOT

28. MCQ: A recent study found that the average life expectancy of a person living in Africa is 53 years with a standard deviation of 7.5 years. If a person in Africa is selected at random, what is the probability that the person lives longer than 60 years? Assume a normal distribution.
a) 0.0243 b) 0.1753 c) 0.3247 d) 0.8247 e) NOT

29. MCQ: At Southwest Nursing School, the average score for an entrance exam is 150, with a standard deviation of 17 points. The scores distribute normally. If the nursing school can only accept the top 10% of the applicants, what is the cutoff score a nurse must make on the entrance exam to be considered for this school?
a) 155 or above. b) 163 or above. c) 172 or above.
d) 181 or above. e) NOT

30. MCQ: In a given normal distribution, if the mean is 500 and 3.62% of the distribution lies to the left of 428, what is the standard deviation for this distribution, correct to the nearest integer?
a) 20 b) 30 c) 40 d) 50 e) NOT

31. MCQ: A report on egg consumption, which distributes normally, shows that people living in China eat an average of 196 eggs each year, with a standard deviation of 18.3 eggs. If a group of 81 Chinese people are selected at random, what is the probability that that the average egg consumption of this group will be greater than 198 eggs?
a) 0.1627 b) 0.1941 c) 0.2344 d) 0.2715 e) NOT

32. MCQ: A recent report stated that 78% of U.S. teens are not asked for identification when they buy cigarettes. If 200 teens who just purchased cigarettes are randomly selected, what is the probability that at most 150 teens were able to purchase cigarettes without being asked for identification?
a) 0.1421 b) 0.1739 c) 0.2051 d) 0.2219 e) NOT

33. MCQ: A research company stated that 20% of missed school days are due to asthma. If a group of 400 school children are selected at random, what is the probability that, at most, 99 children will miss school because of asthma?
a) 0.8765 b) 0.8943 c) 0.9347 d) 0.9926 e) NOT

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Set of probability questions are solved in detail.

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