THE NORMAL DISTRIBUTION, OTHER CONTINUOUS
DISTRIBUTIONS, AND SAMPLING DISTRIBUTION
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.
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 within
±
1 standard deviation from the mean.
c)
It is a discrete probability distribution.
d)
Its parameters are the mean,
μ
, and standard deviation,
σ
.
3.
If a particular batch of data is approximately normally distributed, we would find that
approximately
a)
2 of every 3 observations would fall between
±
1 standard deviation around the mean.
b)
4 of every 5 observations would fall between
±
1.28 standard deviations around the
mean.
c)
19 of every 20 observations would fall between
±
2 standard deviations around the mean.
d)
all of the above
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.
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.
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.

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For some positive value of
X
, the probability that a standardized normal variable is between 0
and
+
2
X
is 0.1255. The value of
X
is
a)
0.99.
b)
0.40.
c)
0.32.
d)
0.16.
8.
For some positive value of
X
, the probability that a standardized normal variable is between 0
and +1.5
X
is 0.4332. The value of
X
is
a)
0.10.
b)
0.50.
c)
1.00.
d)
1.50.
9.
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 hang up before placing an order?
a)
0.22313
b)
0.48658
c)
0.51342
d)
0.77687
10. 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 1.5 minutes will hang up before placing an order?
a)

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