# normal distribution help

#### wanye

##### New Member
A worker earns $15 per hr at a plant and is told that only 2.5% of all workers make a higher wage. If the wage is assumed to be normally distributed and the standard deviation of the wage rate is$5 per hr. Is the average wage for the plant $7.50 per hr? For only 2.5% of all workers to have higher wage than$15, the correct answer for average wage shld be \$5.20 instead?

I am working backwards to retrieve the answer, using a normal distribution calculator, using 15 as the start point, 100000 as the end point.

Pls guide me whether I am working in the correct direction, and one thing is how do i manually calculate the 2.5% possibility using the formula?

#### galactus

##### New Member
1-0.025=0.975. Look up 0.975 in the body of the z-table, see what z-score sorresponds, then use the z-formula. Solve for x.

#### wanye

##### New Member
hi, but u dint told me whether my answer for the average wage is correct?

#### wanye

##### New Member
hey, can someone pls explain in clear value?
If z=(data_value-mean)/(stand_dev),
what's the data value in this sense, x? I thought x=15? If not, what's 15 then? Isnt the average wage the mean ?