Tom went on a bike to the store 3 miles away. If it took Tom 1/2 of an hour to get there and 2/3 of an hour to get back , what w
1 answer:
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Answer:
a)
So we expected about 75% within two deviations from the mean
b)
So we expected about 55.6% within 1.5 deviations from the mean
And the limits are:
c) We can calculate how many deviations we are within the mean with the limits with this formula:
And using the lower limit we got:
And with the upper limit we got:
So then the value of k =4 and the percentage is given by:
Step-by-step explanation:
Previous concepts and Data given
reprsent the population mean
represent the population standard deviation
The Chebyshev's Theorem states that for any dataset
• We have at least 75% of all the data within two deviations from the mean.
• We have at least 88.9% of all the data within three deviations from the mean.
• We have at least 93.8% of all the data within four deviations from the mean.
Or in general words "For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least:
Part a
For this case we can find the percentage required replaincg k =2 and we got:
So we expected about 75% within two deviations from the mean
Part b
For this case we can find the percentage required replaincg k =2 and we got:
So we expected about 55.6% within 1.5 deviations from the mean
And the limits are:
Part c
We can calculate how many deviations we are within the mean with the limits with this formula:
And using the lower limit we got:
And with the upper limit we got:
So then the value of k =4 and the percentage is given by: