SOLUTION: The average weight of a box at a store is 10lbs. with a standard deviation of 2 lbs. If 200 boxes are at the store approximately how many boxes will be between 10 and 13 lbs.

Question 47667: The average weight of a box at a store is 10lbs. with a standard deviation of 2 lbs. If 200 boxes are at the store approximately how many boxes will be between 10 and 13 lbs.
Found 2 solutions by venugopalramana, Nate:
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
The average weight of a box at a store is 10lbs. with a standard deviation of 2 lbs. If 200 boxes are at the store approximately how many boxes will be between 10 and 13 lbs.
10 AND 13 CORRESPOND TO A DEVIATION OF +3 FROM MEAN OF 10 SINCE 13=10+3
DEVIATION OF 3 IS 1.5 TIMES THE STANDARD DEVIATION OF 2 SINCE 2*1.5=3
FROM NORMAL DISTRIBUTION IT IS EXPECTED THAT ABOUT 86% WILL BE BETWEEN -1.5 S.D TO +1.5 S.D AROUND THE MEAN
THAT IS 86% ARE BETWEEN 10-3=7 AND 10+3=13...OR..43% WILL BE BETWEEN 10 AND 13
HENCE APPROXIMATELY 200*43/100=86 BOXES MAY BE BETWEEN 10 AND 13 LBS.
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
sd = standard deviation
average(mean) = m
<--(2%)--(m - 2(sd))--(14%)--(m - sd)--(34%)--(m)--(34%)--(m + sd)--(14%)--(m + 2(sd))--(2%)-->
<--(2%)--(6)--(14%)--(8)--(34%)--(10)--(34%)--(12)--(14%)--(14)--(2%)-->
From 10 to 13 is 1.5 standard deviations: 34% + (1/2)14% = 34% + 7% = 41%
200 boxes * 41% = 82 boxes
RELATED QUESTIONS
Boxes of maraconi are filled by machine and the net weight of a box has a normal... (answered by stanbon)
The weights of newborns are normally distributed with a mean 7 lbs and standard deviation (answered by Boreal)
A manufacturing company measures the weight of boxes before shipping them to the... (answered by stanbon)
If the average weight of three boxes is 3.1 lbs. and two boxes weigh 3.6 lbs. each, what... (answered by macston)
The average weight of a particular box of crackers is 37.0 ounces with a standard... (answered by Boreal)
Based on a sample of 200 textbooks at the store, you find an average of 88.75 and a... (answered by Boreal)
Daily profits at a retail store have an average of $1000. If at least 88.9% of values are (answered by stanbon)
At a large department store, the average number of years of employment for a cashier is... (answered by rothauserc)
At a large department store, the average number of years of employment for a cashier is... (answered by Boreal)