question archive Assume that the reading at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1
Assume that the reading at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1
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Assume that the reading at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P3, the –percentile. This is the temperature reading separating the bottom 3% from the top 97%.
P3 = ---- °C
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We have mean = 0o C and standard deviation = 1o C
We need to find 3rd percentile
z score for 3rd percentile = -1.8808
Using z score formula
z = (x - mean)/sd
-1.8808 = (x - 0)/1
x -0 = -1.8808*1
x = 0 -1.8808
x = -1.8808
x = -1.881 (3 decimals)
Or you can use excel function NORM.INV(area, mean, sd)
setting area = 0.03
mean = 0
standard deviation (sd) = 1
P3 = NORM.INV(0.03, 0, 1)
P3 = -1.881
