Expert: Ahmed Salami - 1/17/2012

Question
The Australian Bureau of 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 48 hours. Based on this percentage, what is the standard deviation of number of hours worked per week for these workers?
[Round your answer to 1 decimal place, the tolerance is +/-0.1].

I could work out on this question except i couldn't find out Z value..Could you explain how to find Z Value of 12% i.e .12

Answer
Hi Pradeep,
We know that z for a value X in a distribution with mean μ and standard deviation σ is
z = X - μ / σ
So, at X = 48
z = (48 - 43.4)/σ
= 4.6/σ
From tables, the z-value for a probability of 0.12 to the right i.e P (X > 48) is 1.175
σ = 4.6/1.175
= 3.91 hours

Working with tables, you need to know that each half of the normal distribution curve represents an area of 0.5 and standard tables usually give the area from 0 to z. In this case where we need the area after z to the right we simply need to subtract the value in the table from 0.5
You should also know that there can be different variations of the normal distribution tables these days and an accompanying diagram would be there to show you the appropriate area the values in the table refer to. The answer you require should always be the same though.

NB: I've attached a picture showing the area corresponding to 0.12 in this case.

Regards