Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.

Question

 A single thermometer is randomly selected and tested. Find P81, the 81-percentile. This is the temperature reading separating the bottom 81% from the top 19%.

Answer 1

Serena

This is a standard normal distribution with μ = 0, σ = 1.

So to find the 81st percentile you need to find X so that the area under the standard normal distribution to the left of x=X is 0.81 (81 %),

So using a table of areas under the standard normal find the area in the table as close as possible to 0.81

Then read off the Z value corresponding to this.

Z = (X-μ) / σ. In this case Z = X. So your 81st percentile will be the Z value

MIKE