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 P₉₄, the 94-percentile. This is the temperature reading separating the bottom 94% from the top 6%.

P₉₄ = _______°C

Answer 1

Use z = (x - μ)/σ or x = zσ + μ

Given: μ = 0 ^oC, σ = 1.00 ^oC

94% = .9400 on a z-table falls half-way between z = 1.55 and z = 1.56 --> z = 1.555

x = 1.555(1.00 ^oC) + 0 ^oC = 1.555 ^oC

P₉₄ = 1.555 ^oC