1. Probability is the

2. A(n) ________________ is a description of how probabilities are distributed over the values of a random variable.

3. An initial estimate of the probabilities of events is a ______________ probability.

4. Bayes’ theorem is a method used to compute ___________________ probabilities.

5. All the events in the sample space that are not part of the specified event are called

6. Sample space is

7. The event containing the outcomes belonging to A or B or both is the ________________ of A and B.

8. Two events are independent if

9. Which statement is true about mutually exclusive events?

10. A joint probability is the

11. In the probability table below, which value is a marginal probability?

12. A variable that can only take on specific numeric values is called a

13. An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a

14. Which of the following statements is correct?

15. Which of the following is a discrete random variable?

16. All of the following are examples of discrete random variables except

17. The _______________ probability distribution can be used to estimate the number of vehicles that go through an intersection during the lunch hour.

18. The random variable X is known to be uniformly distributed between 2 and 12. Compute E(X), the expected value of the distribution.

19. The random variable X is known to be uniformly distributed between 2 and 12. Compute the standard deviation of X.

20. If a zscore is zero, then the corresponding xvalue must be equal to the

21. In a normal distribution, which is greater, the mean or the median?

22. The center of a normal curve is

23. Which of the following is not a characteristic of the normal probability distribution?

24. A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. What percent of the time does he exceed 13,000 steps?

25. The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What is the probability that, if driven normally, the car will get 100 miles per gallon or better?

26. A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 15,000 steps. What was his percentile on that day?

27. The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What value represents the 50^{th} percentile of this distribution?

28. A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution?

29. What is the mean of x, given the exponential probability function

30. Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability density function for the time it takes to fill an order?

31. What is the total area under the normal distribution curve?

32. The triangular distribution is a good model for____________ distributions.

33. Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that The time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes less than one minute to fill an order?

34. A nickel and a dime are tossed. How many possible outcomes are in this event?

35. A nickel and a dime are tossed. We are interested only in the event that includes at least one head appears on a single toss of both coins. What are the possible outcomes?

36. Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What are the possible outcomes for the event of rolling a 7?

37. Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a 7?

38. Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a sum larger than 10?

39. James has two fair coins. When he flips them, what is the sample space?

40. A nickel and a dime are tossed. If an event is defined as a single toss of both coins where at least one head appears, what is the complement of that event?

41. Given that A and B are independent with P(A ∪ B) = 0.8 and P(B^{c}) = 0.3, find P(A).

42. A bucket contains 2 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and then replaced. Another ball is taken from the bucket. Are the events of pulling first ball is red then a purple one independent or dependent?

43. A bucket contains 2 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and then replaced. Another ball is taken from the bucket. What is the probability that the first ball is red and the second ball is purple?

44. A bucket contains 3 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and is not replaced. Another ball is taken from the bucket. Are the events of pulling first ball is red then a purple one independent or dependent?

45. A bucket contains 3 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and is not replaced. Another ball is taken from the bucket. What is the probability that the first ball is red and the second ball is purple?

46. Given that P(A) = 0.3, P(AB) = 0.4, and P(B) = 0.5, compute P(A ∩ B)

47. The cross tabulation below classifies employees of a communications company by age and field of expertise. Use the given information to create a joint probability table.

48. The contingency table below represents employees of a communications company classified by age and field of expertise. Fill in the missing entries.

49. The contingency table below represents employees of a communications company classified by age and field of expertise. What is the probability that a randomly selected employee age 3545 years old has business expertise?

50. The cross tabulation shown below shows employees of a communications company classified by age and field of expertise. What is the probability that a randomly selected engineer is under the age of 35?

51. The random variable X is known to be uniformly distributed between 2 and 12. Compute P(X = 3).

52. The random variable X is known to be uniformly distributed between 2 and 12. Compute P(X > 10).

53. For the standard normal probability distribution, what percent of the curve lies to the left of the mean?

54. Participants at the state fair were given 8 rings to toss. The number x of rings tossed onto a stick can be approximated by the probability distribution in the table. Use the probability distribution to find the mean and variance of the probability distribution.

55. In a binomial experiment, what does it mean to say that each trial is independent of the other trials?

56. What type of distribution models the number of occurrences of an event over a specified interval of time or space?

57. Let X be a random variable with a Uniform distribution between 8 and 20. Find the probability that X is less than 10?

58. Could this curve represent a normal distribution?

59. You recently took a standardized test in which scores follow a normal distribution with a mean of 18 and a standard deviation of 3. You were told that your score is at the 75^{th} percentile of this distribution. What is your score?

60. The time in seconds that it takes a production worker to inspect an item has an exponential distribution with mean 15 seconds. What proportion of inspection times is less than 10 seconds?

61. The random variable X is normally distributed with mean of 80 and standard deviation of 10. What is the probability that a value of X chosen at random will be between 70 and 90?

62. Reviews of call center representatives over the last 3 years showed that 10% of all call center representatives were rated as outstanding, 75% were rated as excellent/good, 10% percent were rated as satisfactory, and 5% were considered unsatisfactory. For a sample of 10 reps selected at random, what is the probability that two will be rated as unsatisfactory?

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