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CHAPTER 9 SECTION 2: SAMPLING DISTRIBUTIONS
MULTIPLE CHOICE
90.
Given that
X
is a binomial random variable with very large
n
, the binomial probability
P
(
X
≥
5) is
approximated by the area under a normal curve to the right of
a.
4.5
b.
5.5
c.
4
d.
6
ANS: A
PTS:
1
REF:
SECTION 9.2
91.
Given that
X
is a binomial random variable with very large
n
, the binomial probability
P
(
X
=
5
) is
approximated by the area under a normal curve between
a.
5 and 5
b.
4 and 6
c.
4.5 and 5.5
d.
None of these choices.
ANS: C
PTS:
1
REF:
SECTION 9.2
92.
Given that
X
is a binomial random variable with very large
n
, the binomial probability
P
(
X
≤
5) is
approximated by the area under a normal curve to the left of
a.
5
b.

5
c.
5.5
d.
4.5
ANS: C
PTS:
1
REF:
SECTION 9.2
93.
As a general rule, the normal distribution is used to approximate the sampling distribution of the sample
proportion only if:
a.
the sample size
n
is greater than 30.
b.
the population proportion
p
is close to 0.50.
c.
the underlying population is normal.
d.
np
and
n
(1

p
) are both greater than or equal to 5.
ANS: D
PTS:
1
REF:
SECTION 9.2
94.
Given a binomial distribution with
n
trials and probability
p
of a success on any trial, a conventional
rule of thumb is that the normal distribution will provide an adequate approximation of the binomial
distribution if
a.
np
≥
5 and
n
(1

p
)
≥
5
b.
np
≥
5 and
np
(1

p
)
≥
5
c.
np
≤
5 and
n
(1

p
)
≤
5
d.
None of these choices.
ANS: A
PTS:
1
REF:
SECTION 9.2
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95.
A sample of size 200 is taken at random from an infinite population. Given that the population
proportion is 0.60, the probability that the sample proportion is greater than 0.58 is:
a.
0.281
b.
0.719
c.
0.580
d.
0.762
ANS: A
PTS:
1
REF:
SECTION 9.2
96.
A sample of size 200 is taken at random from an infinite population. Given that the population
proportion is 0.60, the probability that the sample proportion is less than 0.58 is
a.
0.281
b.
0.719
c.
0.580
d.
0.762
ANS: B
PTS:
1
REF:
SECTION 9.2
97.
A sample of size 200 is taken at random from an infinite population. Given that the population
proportion is 0.60, the probability that the sample proportion is between 0.58 and 0.62 is:
a.
0.4314
b.
0.0320
c.
0.0200
d.
None of these choices.
ANS: A
PTS:
1
REF:
SECTION 9.2
98.
Suppose that the probability
p
of success on any trail of a binomial distribution equals 0.90. Then for
which of the following number of trials,
n,
would the normal distribution provide a good approximation
to the binomial distribution?
a.
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 Spring '10
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