Test Bank: Introduction to Probability and Statistics
True/False
Questions
- The standard deviation of any normal random variable is always equal to one. Answer: False Type: Concept Difficulty: Easy
- For any normal random variable, the probability that the random variable will equal one is always zero. Answer: True Type: Concept Difficulty: Medium
- The graph of a standard normal random variable is always symmetric. Answer: True Type: Concept Difficulty: Easy
- The formula will convert any normal distribution into the “standard normal distribution. ” Answer: True Type: Concept Difficulty: Easy
- Any normal random variable with a standard deviation equal to one is a standard normal random variable. Answer: False Type: Concept Difficulty: Medium
- The notation X – N(4, 32) indicates a normal distribution with mean 2 and standard deviation
- The total area under a normal curve is always equal to one. Answer: True Type: Concept Difficulty: Easy
- The notation Z – N(0, 1) indicates a standard normal distribution. Answer: True Type: Concept Difficulty: Easy
- The probability that a normal random variable will be within two standard deviations of its mean is approximately 0. 8. Answer: False Type: Concept Difficulty: Easy
- The normal distribution is a continuous distribution. Answer: True Type: Concept Difficulty: Easy
- The normal distribution can be used to approximate the binomial distribution when both np and n(1 – p) are at least five. Answer: True Type: Concept Difficulty: Easy
- The normal distribution approximation to the binomial works best when n is large. Answer: True Type: Concept Difficulty: Easy
- The formula can be used with both a normal and binomial distribution. Answer: True Type: Concept Difficulty: Easy Multiple Choice
Questions 4.
- Find P(-2 < Z < 2).
- A)0. 9544
- B)0. 4772
- C)0. 9772
- D)0. 6826
- E)none of the above
Answer: A Type: Computation Difficulty: Easy
Find P(-0. 5 < Z < 0. 5).
- A)0. 3830
- B)0. 1915
- C)0. 6515
- D)0. 3085
- E)None of the above
Answer: A Type: Computation Difficulty: Easy
What is the probability that a standard normal variable will be between -0. 5 and 1. 00?
- A)0. 2857
- B)0. 5328
- C)0. 6687
- D)0. 2500
- E)none of the above
Answer: B Type: Computation Difficulty: Easy
Find the probability that a standard normal random variable has a value greater than -1. 56.
- A)0. 0332
- B)0. 0594
- C)0. 9406
- D)0. 9668
- E)none of the above
Answer: C Type: Computation Difficulty: Easy
Let X be a normally distributed random variable with mean 100 and standard deviation. Find two values, a and b, symmetric about the mean, such that the probability of the random variable being between them is 0. 99.
- A)90. 5, 105. 9
- B)80. 2, 119. 8
- C)22, 78
- D)48. 5, 151. 5
- E)90. 1, 109. 9
Answer: D Type: Computation Difficulty: Medium
A professor grades his students on a normal distribution, with a mean of 75 and a standard deviation. If there are 39 students in his class, about how many scores between 80 and 90?
- A)5
- B)21
- C)8
- D)13
- E)none of the above
Answer: C Type: Computation Difficulty: Hard.
A calculator manufacturer performs a test on its calculators and finds their working life to be normally distributed, with a mean of 2,150 hours and a standard deviation of 450 hours. What should the manufacturer advertise as the life of the calculators so that 90% of the calculators are covered?
- A)2,555
- B)1,947
- C)1,410
- D)1,745
- E)1,574
Answer: E Type: Computation Difficulty: Hard
You have two stocks: A and B. The price of each stock is normally distributed. Stock A has a mean of 25 and a standard deviation of 3. Stock B also has a mean of 25, but the standard deviation is 5. If I buy stock A at $25 and sell it on a randomly chosen day in the future (without knowing its price then), what is the probability that I will make at least $2 on each share? Answer the same for stock B.
- A)0. 2514, 0. 1554
- B)0. 2514, 0. 3446
- C)0. 2486, 0. 1554
- D)0. 2486, 0. 3446
- E)none of the above
Answer: B Type: Computation Difficulty: Hard
Find two values symmetric around a mean of 20 such that they include an area equal to 0. 75. (standard deviation = 5).
- A)16. 65, 23. 35
- B)19. 25, 20. 75
- C)16. 25, 23. 75
- D)14. 25, 25. 75
- E)none of the above
Answer: D Type: Computation Difficulty: Hard
A spark plug manufacturer believes that his plug lasts an average of 30,000 miles, with a standard deviation of 2,500 miles. What is the probability that a given spark plug of this type will last 37,500 miles before replacement?
- A)0. 0228
- B)0. 0114
- C)0. 0013
- D)0. 0714
- E)0. 0833
Answer: C Type: Computation Difficulty: Medium
Fluctuations in the exchange rate of dollars against the pound sterling over a short time period were approximated by a normal distribution with a mean of 2. 01 and a standard deviation of 0. 13. What is the probability that the rate on a particular day was more than 1. 90?
- A)0. 8461
- B)0. 3023
- C)0. 8023
- D)0. 3461
- E)none of the above
Answer: C Type: Computation Difficulty: Medium
The average time it takes for a letter in the United States to reach from one place in the 48 contiguous states to another is 3. 2 days, with a standard deviation of 0. 85 days. What is the probability of a letter arriving at its destination no more than four days after mailing? Assume a normal distribution.
- A)0. 1736
- B)0. 3264
- C)0. 8264
- D)0. 6736
- E)0. 6528
Answer: C Type: Computation Difficulty: Medium
The contents of a particular bottle of shampoo marked as 150 ml are found to be 153 ml at an average, with a standard deviation of 2. 5 ml. What proportion of shampoo bottles contain less than the marked quantity? Assume a normal distribution.
- A)0. 2192
- B)0. 1151
- C)0. 4452
- D)0. 0548
- E)none of the above
- Answer: B Type: Computation Difficulty: Medium
The age of people in a town is normally distributed, with a mean of 34 years and a standard deviation of 11 years. Find two values for an age that will give an asymmetric 0. 95 probability interval.
- A)28. 78, 39. 23
- B)32. 30, 66. 30
- C)23. 55, 44. 45
- D)12. 44, 55. 56
- E)15. 91, 51. 10
Answer: D Type: Computation Difficulty: Medium
The weight of apples in a farm is normally distributed, with a mean of 110 grams, and a standard deviation of 15 grams. Find the probability that an apple selected at random will weigh between 95 and 105 grams.
- A)0. 3413
- B)0. 4706
- C)0. 1293
- D)0. 2108
- E)0. 5294
Answer: D Type: Computation Difficulty: Medium
A grocery store has a mean account receivable of $264, with a standard deviation of $55. The accounts receivable are normally distributed. What proportion of all accounts will be greater than $275?
- A)0.
- B)0. 1
- C)0. 4207
- D)0. 0793
- E)0. 0228
Answer: C Type: Computation Difficulty: Medium
A grocery store has a mean account receivable of $264, with a standard deviation of $55. The accounts receivable are approximately normally distributed. Find the value such that 45% of all the accounts exceed this value. That is, find x such that: P(X > x) = 0. 45.
- A)$257. 13
- B)$354. 48
- C)$270. 91
- D)$309. 00
- E)none of the above
Answer: C Type: Computation Difficulty: Medium 31. The waist measurement of students in a college is normally distributed. The standard deviation is known to be five inches.
It is found that 15% of the students have waist sizes less than 28 inches. What proportion of students will have waists between 30 and 35 inches?
- A)0. 3795
- B)0. 2389
- C)0. 1406
- D)0. 0983
- E)None of the above
Answer: A Type: Computation Difficulty: Hard
The IQs of the employees of a company are normally distributed, with a mean of 127 and a standard deviation of 11. What is the probability that the IQ of an employee selected at random will be between 120 and 130?
- A)0. 2389
- B)0. 3453
- C)0. 1064
- D)0. 1325
- E)0. 4638
Answer: B Type: Computation Difficulty: Medium 33.
For a normally distributed random variable with mean zero and standard deviation five, the probability that its value will be greater than -5 is:
- A)0. 4772
- B)0. 9544
- C)0. 3413
- D)0. 8413
- E)None of the above
Answer: D Type: Computation Difficulty: Medium
What is the probability that a standard normal random variable is between -0. 4 and 1. 4?
- A)0. 3413
- B)0. 4254
- C)0. 5746
- D)0. 2638
- E)None of the above
Answer: C Type: Computation Difficulty: Easy
All of the following are characteristics of the normal distribution, except:
- A) symmetric about the mean
- B) bell-shaped curve
- C) total area under the curve is always one
- D) it is a discrete distribution
- E) probability that x is equal to any specific value is zero
Answer: D Type: Computation Difficulty: Medium
Find two values symmetric about a mean of 100, the standard deviation of 10, such that they include an area equal to 0. 95.
- A)90, 110
- B)80. 4, 119. 6
- C)98. 04, 101. 96
- D)70, 130
- E)none of the above
Answer: B Type: Computation Difficulty: Medium
A tire manufacturer believes its tires will last an average of 48,000 miles, with a standard deviation of 2,000 miles. What is the probability that one of these tires, chosen at random, will last at least 50,000 miles?
- A)0. 6587
- B)0. 3413
- C)0. 1587
- D)0. 4772
- E)none of the above
Answer: C Type: Computation Difficulty: Medium
Suppose that an instructor gives an exam. This instructor wants to give those students in the top 2. 5% an A on this exam. What will the cutoff be for an A, if the average score on this exam is 80, with a standard deviation of 5?
- A)about 80
- B)about 90
- C)about 85
- D)about 86
- E)none of the above
Answer: B Type: Computation Difficulty: Hard Use the following to answer questions 51-54: LittleAir operates a fleet of regional jets on a contract basis for a major air carrier.
