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The 95th percentile for the average number of residents within five miles of each store is 20219.86.
Given mean of 19000 , sample size of 75 stores and standard deviation of 7600.
We have to find the 95th percentile for the average number of residents within five miles of each store in a sample of 75 stores.
We have to first find the margin of error to calculate the upper level of confidence interval.
Margin of error is the difference between the real values and calculated values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is the critical value of z at given confidence level.
σ is standard deviation
n is the sample size.
z value at 95% confidence level is 1.39. (one tailed)
Put the values in the formula to get margin of error.
Margin of error=1.39*7600/[tex]\sqrt{75}[/tex]
=10564/8.66
=1219.86
Upper level=19000+1219.86
=20219.86
Hence the 95th percentile is 20219.86 for the average number of residents within five miles of each store in a sample of 75 stores.
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