An Internet provider\'s report on the times that its customers stayed connected

Question

An Internet provider's report on the times that its customers stayed connected to the internet during a particular holiday have the following numerical descriptive measures (summary statistics) on connection times: 3th-Percentile = 22 minutes 90th-Percentile = 58 minutes Median = 36 minutes Mean = 42 minutes Mode = 33 minutes Range = 24 minutes Standard Deviation = 9 minutes a. The above information indicates that the 3th-percentile, and the 90the-percentile are 22 and 58 minutes; respectively. Based on these information, in that holiday, what percentage of this provider's customers stayed connected to the internet between 22 and 58 minutes? Work: b. Note that the mean and standard deviation of connections times were mean-42 minutes and standard deviation- 9 minutes. According to the Tchebysheff's theorem, at least what percentage of this provider's customers stayed connected to the internet between 6 and 78 minutes in that holiday? Work: c. Suppose we find out that in the Report, each connection time figure by mistake was over-reported by 10 minutes. That is, the true connection time for each customer is 10 minutes less than what was recorded. Suppose we make the correction for each connection time figure (that is, subtract 10 from each connection time). Use the effect of this correction on the above descriptive measures and give the corrected value on the appropriate dotted lines: Corrected Value of the 90th-Percentile:_____ Corrected Value of the Median: ______ Corrected Value of the Mean:_________ Corrected Value of the Mode:____________________ Corrected Value of the Range:________ Corrected Value of the Standard Deviation:______

Explanation / Answer

a)% stayed in b/w 90th and 3rd percentile =90-3=87 %

b)as 6 and 78 are 4 std deviaion away from mean.

hence as per chebyshev's % of customer stayed b/w 6min and 78 min=(1-1/k2 )*100(1/(4)2 )*100=1500/16=93.75%

3) 90th percentile =58-10=48

median=36-10=26

mean =42-10=32

mode=23 minures

range =24 minutes; as both minimumm and maximum increased by same amount hence no effect

std deviation =9 minutes, as both mean and individual increased by same amount hence no effecr

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