Question 344944: Please answer this question. I am having difficulty understanding this course my Professor does not speak English well, and has problems explaining the steps to the class.
Thank you
The following frequency distribution reports the electricity cost for a sample of 50 two-bedroom apartments in Albuquerque, New Mexico during the month of May last year.
Electricity Cost Frequency
$80 up to $100 3
100 up to 20 8
120 up to 140 12
140 up to 160 16
160 up to 180 7
180 up to 200 4
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Total 50
a. Estimate the mean cost.
b. Estimate the standard deviation.
c. Use the Empirical Rule to estimate the proportion of costs within two standard deviations of the mean. Waht are these limits?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The following frequency distribution reports the electricity cost for a sample of 50 two-bedroom apartments in Albuquerque, New Mexico during the month of May last year.
Comment: When you are given a frequency distribution, you have to use the
"Mark" of each category as the representative value for the numbers in
that category.
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Electricity Cost Frequency
$80 up to $100 3 ::::: Mark = (100+80)/2 = 90
100 up to 120 8 ::::: Mark = (120+100)/2 = 110
120 up to 140 12 ::::: Mark = (120+140)/2 = 130
140 up to 160 16 ::::: Mark = 150
160 up to 180 7 ::::: Mark = 170
180 up to 200 4 ::::: Mark = 190
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Total 50
a. Estimate the mean cost.
mean = [3*90+8*110+12*130+16*150+7*170+4*190)/(sum of the freqs) = 141.2
Note: I used a TI-84 to get that mean value.
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b. Estimate the standard deviation.
S = 26.236
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c. Use the Empirical Rule to estimate the proportion of costs within two standard deviations of the mean. What are these limits?
mean - 2*S = 141.2-2*26.236 = 87.728
mean + 2*S = 141.2+2*26.236 = 192.672
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Cheers,
Stan H.
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