The values of bills for the last 12 months 338.28 328.93 341.03331.29356.01329.03328.46586.34401.23386.37388.43367.31A) Find the sample mean and sample standard deviation of your data.B) Pick three bills from the last 12 months and change the values into z-scores. What does the z-score tell you about that particular month?C) Between what two values would be considered a normal bill? Remember, being within 2 Standard Deviations is considered normal.

Question

03-11-2022
Mathematics

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The values of bills for the last 12 months 338.28 328.93 341.03331.29356.01329.03328.46586.34401.23386.37388.43367.31A) Find the sample mean and sample standard deviation of your data.B) Pick three bills from the last 12 months and change the values into z-scores. What does the z-score tell you about that particular month?C) Between what two values would be considered a normal bill? Remember, being within 2 Standard Deviations is considered normal.

Answer :

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MaxT247558 MaxT247558 · Answer 1 · 2022-11-03T07:21:40-04:00

step 1

Find out the mean

we have the data set

Mean=(338.28+328.93+341.03+331.29+356.01+329.03+328.46+586.34+401.23+386.37+388.43+367.31)/12

Mean=(4,482.71)/12

Mean=373.56

step 2

Find out the sample standard deviation

Subtract the mean from each data point and square it

(338.28-373.56)^2=1244.6784

(328.93-373.56)^2=1991.8369

(341.03-373.56)^2=1058.2009

(331.29-373.56)^2=1786.7529

(356.01-373.56)^2=308.0025

(329.03-373.56)^2=1982.9209

(328.46-373.56)^2=2034.01

(586.34-373.56)^2=45275.3284

(401.23-373.56)^2=765.6289

(386.37-373.56)^2=164.0961

(388.43-373.56)^2=221.1169

(367.31-373.56)^2=39.0625

Add the squared deviations

S=56,871.6353

Divide by the number of data sets minus 1

S/(n-1)

where

n=12

56,871.6353/(12-1)=5,170.14866

Take the square root

sample standard deviation=√(5,170.14866)

sample standard deviation=71.90

Part B

Remember that

z =(x - μ)/s

where

μ=373.56

s=71.90

I take the bills