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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
≈ 1 − P(Z ≤
= 1 − P(Z ≤ ) = 1 − 0.5675 = 0.4325.
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, multi-modal, 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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