Question

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

Find P₁, the 1-percentile of the distribution of temperature readings. This is the temperature reading separating the bottom 1% from the top 99%.

°C Round to 2 places.

Answer 1

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

Hence to calculate the 1 percentile value for this distribution hence we need to find the Z score for 1 percentile which can be calculated using the excel formula for normal distribution which is =NORM.S.INV(0.01), thus the Z-score computed is -2.326.

Z = -2.326

Now the based on the Z score mathematical formula the 1 percentile value is calculated as:

Hence the 1-percentile value would be -2.33 °C.