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Homework help - how to find the standard deviation? (10 points for best answer!)?
Weakly earnings on a certain import venture are approximately normally distributed with a known mean of $488 and unknown standard deviation. If the proportion of earnings over $502 is 34%, find the standard deviation. Answer only up to two digits after decimal.
I have tried this multiple times and I still have no idea how to do this. Any help would be appreciated!
1 Answer
- AlanLv 71 year ago
P(X> 502) = 1 -P(x< 502)
0.34 = 1- P(x<502)
P(x< 502) = 1- 0.34 = 0.66
so look up Z value for
P(z<Z) = 0.66
P(z< 0.41 ) = 0.65910
P(z< 0.42 ) = 0.66276
0.41 + (0.66 -0.6591) * 0.01/ (0.66276-0.65910)
Z value = 0.412459016 =0.4125 approx.
Z = (x-mean)/standard deviation
Z*standard deviation = x -mean
standard deviation = (x-mean)/ Z = (502-488)/ 0.4125 = 33.93939394
=== My Answer (and most correct answer)
standard deviation = 33.94 (rounded to two digits after the decimal)
alternate answer if they expect you to use the closest Z value
if they expect you to just us the closest Z value ,
it would be Z= 0.41, then SD = 14/0.41 = 34.15