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York University

Management

MGMT 1050

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142 The Normal Distribution and Other Continuous Distributions
CHAPTER 6: THE NORMAL DISTRIBUTION AND OTHER
CONTINUOUS DISTRIBUTIONS
1. In its standardized form, the normal distribution
a) has a mean of 0 and a standard deviation of 1.
b) has a mean of 1 and a variance of 0.
c) has an area equal to 0.5.
d) cannot be used to approximate discrete probability distributions.
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: standardized normal distribution, properties
2. Which of the following about the normal distribution is NOT true?
a) Theoretically, the mean, median, and mode are the same.
b) About 2/3 of the observations fall wi1 standard deviation from the mean.
c) It is a discrete probability distribution.
d) Its parameters are the mean, and standard deviation.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: normal distribution, properties
3. If a particular batch of data is approximately normally distributed, we would find that
approximately
a) 2 of every 3 observations would fall bet1 standard deviation around the mean.
b) 4 of every 5 observations would fall bet1.28 standard deviations around the mean.
c) 19 of every 20 observations would fall betw2 standard deviations around the mean.
d) all of the above
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: normal distribution, properties 143 The Normal Distribution and Other Continuous Distributions
4. For some positive value of Z, the probability that a standardized normal variable is between 0 and
Z is 0.3770. The value of Z is
a) 0.18.
b) 0.81.
c) 1.16.
d) 1.47.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: standardized normal distribution, value
5. For some value of Z, the probability that a standardized normal variable is below Z is 0.2090. The
value of Z is
a) – 0.81.
b) – 0.31.
c) 0.31.
d) 1.96.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: standardized normal distribution, value
6. For some positive value of Z, the probability that a standardized normal variable is between 0 and
Z is 0.3340. The value of Z is
a) 0.07.
b) 0.37.
c) 0.97.
d) 1.06.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: standardized normal distribution, value
7. For some positive value of X, the probability that a standardized normal variable is between0 and
+2X is 0.1255. The value of X is
a) 0.99.
b) 0.40.
c) 0.32.
d) 0.16.
ANSWER:
d
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: normal distribution, value The Normal Distribution and Other Continuous Distributions 144
8. For some positive value of X, the probability that a standardized normal variable is between0 and
+1.5X is 0.4332. The value of X is
a) 0.10.
b) 0.50.
c) 1.00.
d) 1.50.
ANSWER:
c
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: normal distribution, value
9. Given that X is a normally distributed random variable with a mean of 50 and a standard deviation
of 2, find the probability that X is between47 and 54.
ANSWER:
0.9104
TYPE: PR DIFFICULTY: Easy
KEYWORDS: normal distribution, probability
10. A company that sells annuities must base the annual payout on the probability distribution of the
length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of
the participants is approximately a normal distribution with a mean of 68 years and a standard
deviation of 3.5 years. What proportion of the plan recipients would receive payments beyond age
75?
ANSWER:
0.0228
TYPE: PR DIFFICULTY: Easy
KEYWORDS: normal distribution, probability
11. A company that sells annuities must base the annual payout on the probability distribution of the
length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of
the participants is approximately a normal distribution with a mean of 68 years and a standard
deviation of 3.5 years. What proportion of the plan recipients die before they reach the standard
retirement age of 65?
ANSWER:
0.1957
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: normal distribution, probability 145 The Normal Distribution and Other Continuous Distributions
12. A company that sells annuities must base the annual payout on the probability distribution of the
length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of
the participants is approximately a normal distribution with a mean of 68 years and a standard
deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the
plan participants.
ANSWER:
71.78 years old
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: normal distribution, value
13. A catalog company that receives the majority of its orders by telephone conducted a study to
determine how long customers were willing to wait on hold before ordering a product. The length
of time was found to be a random variable best approximated by an exponential distribution with a
mean equal to 3 minutes. What proportion of customers having to hold more than 4.5 minutes will
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