<PRE><B>Question 1049944</B>
std dev of sample = std dev of the population/ square root of sample size
:
std dev of sample = 3.6 / square root(100)
:
std dev of sample = 3.6 / 10 = 0.36
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we use the 68-95-99.7 rule for 1, 2 , 3 standard deviations
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(a) asks us what is the probability that the error of the estimate for the mean of the sample is greater than 2 standard deviations
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this will be (99.7 - 95) / 2 = 2.35%
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note why did I have to divide by 2?
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(b) asks us what is the probability that the error of the estimate for the mean of the sample is less than 0.45
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0.45 = 0.36 (1 standard deviation) + 0.09 (1/4 of 1 standard deviation)
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this will be (99.7/2) + (68/2) + (95/(4*2)) =  95.725%
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