Show all work A population of line voltages has a standard d

Show all work

A population of line voltages has a standard deviation of 1.20 volts. What value would the mean line voltage have to be so that 12.1% of the line voltages fell below 115V?

Solution

P ( Z < x ) = 0.121
Value of z to the cumulative probability of 0.121 from normal table is -1.17
P( x-u/s.d < x - U/1.2 ) = 0.121
That is, ( 115 - U/1.2 ) = -1.17
--> ( 115 - U ) = -1.17*1.2 = -1.404  
--> U = 115 + 1.404 = 116.404