SOLUTION: the U.S. Bureau of Labour Statistics reports that of persons who usually work full time, the average number of hours worked per week is 43.4. Assume that the number of hours worked

Question 686313: the U.S. Bureau of Labour Statistics reports that of persons who usually work full time, the average number of hours worked per week is 43.4. Assume that the number of hours worked per week for those who usually work full time is normally distributed. Suppose 12% of these workers work more than 48 hours. Based on this, what is the standard deviation of the number of hours worked per week for these workers?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the U.S. Bureau of Labour Statistics reports that of persons who usually work full time, the average number of hours worked per week is 43.4. Assume that the number of hours worked per week for those who usually work full time is normally distributed. Suppose 12% of these workers work more than 48 hours. Based on this, what is the standard deviation of the number of hours worked per week for these workers?
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Draw a picture of the problem using a normal curve.
Put 43.4 at the middle.
Sketch 12% of area to the right of 48 (that area is a right tail)
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Find the z-value that has a left tail of 88%
invNorm(0.88) = 1.1750
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Solve for "s" using x = z*s + u
48 = 1.1750*s + 43.4
s = (48-43.4)/1.1750 = 3.9149
That is the standard deviation.
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Cheers,
Stan H.
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