Suppose that the readings on the thermometers are normally d

Suppose that the readings on the thermometers are normally distributed with a mean of 0 degree and a standard deviation of 1.00 degree C. If 11 % of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others. Use Excel to obtain more accuracy.

Solution

Mean ( u ) =0
Standard Deviation ( sd )=1
Number ( n ) = 41
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P ( Z < x ) = 0.11
Value of z to the cumulative probability of 0.11 from normal table is -1.227
P( x-u/s.d < x - 0/1 ) = 0.11
That is, ( x - 0/1 ) = -1.23
--> x = -1.23 * 1 + 0 = -1.227