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Unformatted text preview: the condition (np > 10),
one might also consider normal approximation to binomial with continuity correction
is adopted for approximation.
P(Y > 10) = 1 − P(Y ≤ 10)
10 + 1 − 10
2
√
≈ 1 − P(Z ≤
)
9
1
= 1 − P(Z ≤ ) = 1 − 0.5675 = 0.4325.
6
67. True or False: (justify/explain your answer)
a. With a large sample, the sample histogram will closely resemble the normal curve.
SOLUTION: False. The sample histogram or its edge line will closely resemble the pmf
or pdf of the underlying distribution (whatever it is, i.e. discrete, multimodal, skewed,...),
as sample size increases.
b. With a large sample, the probability density function of the sample mean will closely
resemble the normal curve.
SOLUTION: True. This can be seen through Central Limit Theorem.
68. Prior ﬁeld surveys indicate that 24% of ﬁsh in a ﬁsh farm are infected with a certain parasite.
Give an approximate probability that, in a random sample of 300 ﬁsh, between 60 and 84
ﬁsh, inclusive, are infected. If, in such a random sample, 85 ﬁsh were found to be infected,
would this provide stro...
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 Fall '11
 DANIELCONUS
 Statistics, Probability, Standard Deviation

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