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.