The gypsy moth is a serious threat to oak and aspen trees. A state agriculture d
ID: 3129634 • Letter: T
Question
The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths per trap is only 1.2, but some traps have several moths. The distribution of moth counts in traps is strongfy right skewed, with standard deviation 1.4. A random sample of 60 traps has x = 1 and s = 2.4. Let X = the number of moths in a randomly selectd trap (a) For the population distribution, what is the... (b) For the distribution of the sample data, what is the... (c) What shape does the distribution of the sample data probably have? Left skewed Exactly Normal Approximately Normal Right skewed (d) For the sampling distribution of the sample mean with n = 60, what is the... (e) What is the shape of the sampling distribution of the sample mean? Approximately Normal Exactly Normal Right skewed Left skewed (f) If instead of a sample size of 60, suppose the sample size were 10 instead.Explanation / Answer
a)
Mean = 1.2
standard deviation = 1.4 [ANSWERS, GIVEN]
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b)
Mean = 1
standard deviation = 2.4 [ANSWERS, GIVEN]
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c)
As the standard deviation is greater than the mean, then it is
OPTION D: RIGHT SKEWED
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D)
By central limit theorem,
Mean = 1.2 [ANSWER], same mean
standard deviation = sigma/sqrt(n) = 1.4/sqrt(60) = 0.181 [ANSWER]
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E)
By central limit theorem,
OPTION A: APPROXIMATELY NORMAL
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f)
It is still similar to the original distribution because the sample size is small,
OPTION B: SOMEWHAT RIGHT SKEWED
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g)
OPTION B: NO, becasue the sampling distribution is somewhat right skewed.
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