A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9. Below you will find normal probability and percentile calculations related to the customer purchase amounts.
Probability Calculations P(Sales < $ 15.00) = 0.048, P(Sales < $ 20.00) = 0.133 P(Sales < $ 25.00) = 0.289, P(Sales < $ 35.00) = 0.711 Percentiles Calculations 1^{st} Percentile = $9.06, 5^{th} Percentile = $15.20 95^{th} Percentile = $44.80, 99^{th} Percentile = $50.94 
1. What two dollar amounts, equidistant from the mean of $30, such that 98% of all customer purchases are between these values?

2. The higher the value of the density function f(x), _____.

3. One reason for standardizing random variables is to measure variables with:

4. If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?

5. The normal distribution is a:

6. The standard deviation of a probability distribution is a measure of:

7. The mean of a probability distribution is a measure of:

8. If we plot a continuous probability distribution f(x), the total probability under the curve is:

9. A continuous probability distribution is characterized by:

10. Which equation shows the process of standardizing?

11. The standard normal distribution has a mean and a standard deviation respectively equal to:

12. Which of the following might not be appropriately modeled with a normal distribution?

13. Given that Z is a standard normal random variable, P(1.0Z1.5) is:

14. Given that Z is a standard normal variable, the value z for which P(Z z) = 0.2580 is:

15. If X is a normal random variable with a standard deviation of 10, then 3X has a standard deviation equal to:

16. Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 X 90) is:

17. The total area under the normal distribution curve is equal to one.

18. If the random variable X is normally distributed with mean and standard deviation , then the random variable Z defined by is also normally distributed with mean 0 and standard deviation 1.

19. Using the standard normal distribution, the Zscore representing the 5th percentile is 1.645.

20. A random variable X is standardized when each value of X has the mean of X subtracted from it, and the difference is divided by the standard deviation of X.

21. Using the standard normal distribution, the Z– score representing the 99th percentile is 2.326.

22. The mean and standard deviation of a normally distributed random variable that has been “standardized” are zero and one, respectively.

23. Using the standard normal curve, the Z– score representing the 75th percentile is 0.674.

24. A random variable X is normally distributed with a mean of 175 and a standard deviation of 50. Given that X = 150, its corresponding Z– score is –0.50.

25. Using the standard normal curve, the Z– score representing the 10th percentile is 1.28.

A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9. Below you will find normal probability and percentile calculations related to the customer purchase amounts.
Probability Calculations P(Sales < $ 15.00) = 0.048, P(Sales < $ 20.00) = 0.133 P(Sales < $ 25.00) = 0.289, P(Sales < $ 35.00) = 0.711 Percentiles Calculations 1^{st} Percentile = $9.06, 5^{th} Percentile = $15.20 95^{th} Percentile = $44.80, 99^{th} Percentile = $50.94 
26. What is the probability that a randomly selected customer will spend less than $15?

27. What is the probability that a randomly selected customer will spend $20 or more?

28. What is the probability that a randomly selected customer will spend $30 or more?

29. What is the probability that a randomly selected customer will spend between $20 and $35?

30. What two dollar amounts, equidistant from the mean of $30, such that 90% of all customer purchases are between these values?

The weekly demand for General Motors (GM) car sales follows a normal distribution with a mean of 40,000 cars and a standard deviation of 12,000 cars. 
31. There is a 5% chance that GM will sell more than what number of cars during the next year?

32. What is the probability that GM will sell between 2.0 and 2.3 million cars during the next year?

The weekly demand for a particular automobile manufacturer follows a normal distribution with a mean of 40,000 cars and a standard deviation of 10,000. Below you will find probability and percentile calculations related to the customer purchase amounts. Use this information to answer the following questions.
Probability Calculations Percentiles Calculations 
33. Calculate the mean, variance, and standard deviation for the entire year (assume 52 weeks in the year).

34. There is a 1% chance that this company will sell more than what number of cars during the next year?

35. What is the probability that this company will sell more than 2 million cars next year?

36. What is the probability that this company will sell between 2.0 and 2.15 million cars next year?

37. What number of cars, equidistant from the mean, such that 90% of car sales are between these values?

38. What number of cars, equidistant from the mean, such that 98% of car sales are between these values?

Wendy’s fastfood restaurant sells hamburgers and chicken sandwiches. Suppose that on a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30. Use this information to answer the following questions. 
39. How many chicken sandwiches must the restaurant stock to be 99% sure of not running out on a given day?

40. If the restaurant stocks 600 hamburgers and 150 chicken sandwiches for a given day, what is the probability that it will run out of hamburgers or chicken sandwiches (or both) that day? Assume that the demands for hamburgers and chicken sandwiches are probabilistically independent.

41. A restaurant stocks 600 hamburgers and 150 chicken sandwiches for a given day. Assume that the demands for hamburgers and chicken sandwiches are probabilistically independent. Why is the independence assumption in this scenario probably not realistic? Using a more realistic assumption, do you think the probability would increase or decrease?

A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8. 
42. What percentage of students scored between 81 and 89 on this exam?

43. What is the probability of getting a score higher than 85 on this exam?

44. Only 5% of the students taking the test scored higher than what value?

45. The density function specifies the probability distribution of a continuous random variable.

46. According to the empirical rule, how many observations lie within +/ 1 standard deviation from the mean?

47. According to the empirical rule, how many observations lie within +/ 2 standard deviation from the mean?

48. According to the empirical rule, how many observations lie within +/ 3 standard deviation from the mean?

Wendy’s fastfood restaurant sells hamburgers and chicken sandwiches. Suppose that on a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30. Use this information to answer the following questions. 
49. How many hamburgers must the restaurant stock to be 99% sure of not running out on a given day?

50. The results of tossing a coin can be portrayed in a(n):

51. We assume that the outcomes of successive trials in a binomial experiment are:

52. Sampling done without replacement means that:

53. The variance of a binomial distribution for which n = 100 and p = 0.20 is:

54. The binomial probability distribution is used with:

55. The variance of a binomial distribution is given by the formula, where n is the number of trials, and p is the probability of success in any trial.

56. The binomial distribution is a continuous distribution that is not far behind the normal distribution in order of importance.

57. The binomial distribution is a discrete distribution that deals with a sequence of identical trials, each of which has only two possible outcomes.

58. A binomial distribution with n number of trials, and probability of success p can be approximated well by a normal distribution with mean np and variance if np > 5 and n(1p) > 5.

59. For a given probability of success p that is not too close to 0 or 1, the binomial distribution tends to take on more of a symmetric bell shape as the number of trials n increases.

60. The binomial random variable represents the number of successes that occur in a specific period of time.

61. The binomial distribution deals with consecutive trials, each of which has two possible outcomes.

62. The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

The height of American male adults is normally distributed with a mean of 68 inches and a standard deviation of 5 inches. We observe the heights of 12 American male adults. 
63. What is the probability that exactly half the male adults will be less than 62 inches tall?

64. Let Y be the number of the 12 male adults who are less than 62 inches tall. Determine the mean and standard deviation of Y.

The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold. 
65. What type of probability distribution will most likely be used to analyze warranty repair needs on new microwaves in this situation?

66. What is the probability that none of the 20 new microwaves sold will require a warranty repair in the first 90 days?

67. What is the probability that exactly two of the 20 new microwaves sold will require a warranty repair in the first 90 days?

68. What is the probability that less than two of the 20 new microwaves sold will require a warranty repair in the first 90 days?

69. What is the probability that at most two of the 20 new microwaves sold will require a warranty repair in the first 90 days?

70. What is the probability that only one of the 20 new microwaves sold will require a warranty repair in the first 90 days?

71. What is the probability that more than one of the 20 new microwaves sold will require a warranty repair in the first 90 days?

72. What is the probability that at least one of the 20 new microwaves sold will require a warranty repair in the first 90 days?

73. What is the probability that between two and four (inclusive) of the 20 new microwaves sold will require a warranty repair in the first 90 days?

74. What is the probability that between three and six (exclusive) of the 20 new microwaves sold will require a warranty repair in the first 90 days?

75. What is the expected number of the new microwaves sold that will require a warranty repair in the first 90 days?

76. What is the standard deviation of the number of the new microwaves sold that will require a warranty repair in the first 90 days?

Consider a binomial random variable X with n = 5 and p = 0.40. 
77. Find the probability distribution of X.

78. Find P(X < 3).

79. Find P(2X4).

80. Find the mean and the variance of X.

A recent survey in Michigan revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. 
81. Describe the probability distribution of X.

82. Find P(X = 10).

83. Find P(4 < X < 9).

84. Find P(X = 2).

85. Find P(3X6).

86. Suppose that an highway patrol officer can obtain radar readings on 500 vehicles during a typical shift. How many traffic violations would be found in a shift?

Past experience indicates that 20% of all freshman college students taking an intermediate algebra course withdraw from the class. 
87. (A) Using the binomial distribution, find the probability that 6 or more of the 30 students taking this course in a given semester will withdraw from the class.
(B) Using the normal approximation to the binomial, find the probability that 6 or more of the 30 students taking this course in a given semester will withdraw from the class. (C) Compare the results obtained in (A) and (B). Under what conditions will the normal approximation to this binomial probability become even more accurate?

A large retailer has purchased 10,000 DVDs. The retailer is assured by the supplier that the shipment contains no more than 1% defective DVDs (according to agreed specifications). To check the supplier’s claim, the retailer randomly selects 100 DVDs and finds six of the 100 to be defective. 
88. (A) Assuming the supplier’s claim is true, compute the mean and the standard deviation of the number of defective DVDs in the sample.
(B) Based on your answer to (A), is it likely that as many as six DVDs would be found to be defective, if the claim is correct? (C) Suppose that six DVDs are indeed found to be defective. Based on your answer to (A), what might be a reasonable inference about the manufacturer’s claim for this shipment of 10,000 DVDs?

89. A Poisson distribution is:

90. The Poisson random variable is a:

91. Which probability distribution applies to the number of events occurring within a specified period of time or space?

92. If the random variable X is exponentially distributed with parameter = 3, then P(X 2) , up to 4 decimal places, is:

93. If the random variable X is exponentially distributed with parameter = 1.5, then P(2X 4), up to 4 decimal places, is:

94. The Poisson and exponential distributions are commonly used in:

95. Which distribution is bestsuited to measure the length of time between arrivals at a grocery checkout counter?

96. If the mean of an exponential distribution is 2, then the value of the parameter is:

97. The number of loan defaults per month at a bank is Poisson distributed.

98. Much of the study of probabilistic inventory models, queuing models, and reliability models relies heavily on the Poisson and exponential distributions.

99. The Poisson probability distribution is one of the most commonly used continuous probability distributions.

100. A Poisson distribution is appropriate to determine the probability of a given number of defective items in a shipment.

101. The Poisson distribution is characterized by a single parameter, which must be positive.

102. An exponential distribution with parameter = 0.2 has mean and standard deviation both equal to 5.

103. The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.

104. The Poisson random variable is a discrete random variable with infinitely many possible values.

Suppose that the number of customers arriving each hour at the only checkout counter at a local convenience store is approximately Poisson distributed with an expected arrival rate of 30 customers per hour. Let X represent the number of customers arriving per hour. The probabilities associated with X are shown below.
P(X < 5) = 0.0000, P(X < 10) = 0.0000, P(X < 15) = 0.0009 P(X < 20) = 0.0219, P(X < 25) = 0.1572, P(X < 30) = 0.4757 P(X = 30) = 0.0726, P(X = 31) = 0.0703, P(X = 32) = 0.0659 P(X = 33) = 0.0599, P(X = 34) = 0.0529, P(X = 35) = 0.0453 
105. What is the probability that at least 25 customers arrive at this checkout counter in a given hour?

106. What is the probability that at least 20 customers, but fewer than 30 customers arrive at this checkout counter in a given hour?

107. What is the probability that fewer than 33 customers arrive at this checkout counter in a given hour?

108. What is the probability that the number of customers who arrive at this checkout counter in a given hour will be between 30 and 35 (inclusive)?

109. What is the probability that the number of customers who arrive at this checkout counter in a given hour will be greater than 35?

The number of arrivals at a local gas station between 3:00 and 5:00 P.M. has a Poisson distribution with a mean of 12. 
110. Find the probability that the number of arrivals between 3:00 and 5:00 P.M. is at least 10.

111. Find the probability that the number of arrivals between 3:30 and 4:00 P.M. is at least 10.

112. Find the probability that the number of arrivals between 4:00 and 5:00 P.M. is exactly two.

A used car salesman in a small town states that, on the average, it takes him 5 days to sell a car. Assume that the probability distribution of the length of time between sales is exponentially distributed. 
113. What is the probability that he will have to wait at least 8 days before making another sale?

114. What is the probability that he will have to wait between 6 and 10 days before making another sale?

The time it takes a technician to fix a computer problem is exponentially distributed with a mean of 15 minutes. 
115. What is the probability density function for the time it takes a technician to fix a computer problem?

116. What is the probability that it will take a technician less than 10 minutes to fix a computer problem?

117. What is the variance of the time it takes a technician to fix a computer problem?

118. What is the probability that it will take a technician between 10 to 15 minutes to fix a computer problem?

A continuous random variable X has the probability density function: f(x) = 2, 0 
119. What is the distribution of X and what are the parameters?

120. Find the mean and standard deviation of X.

121. What is the probability that X is between 1 and 3?

122. What is the probability that X is at most 2?

123. The local police department is interested in estimating the number of cars that fail to stop at a stop sign during a specified lunch hour. Which probability distribution should they use?

124. The library is interested in estimating the number of individuals who use the computers during the lunch hour. Which probability distribution should they use?

125. The public school system is interested in examining the probability of a child being late to school. The child is categorized as either late or not late. What type of distribution should the school use to examine this issue?

There are no reviews yet.