Question

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. A single thermometer is randomly selected and tested. Find P32, the 82-percentile (using GeoGebra). This is the temperature reading separating the bottom 82% from the top 18%. Round your answer to the nearest 1000th if necessary.

Answer 1

Answer: To find the temperature reading separating the bottom 82% from the top 18%, we need to find the z-score that corresponds to the 82nd percentile, and then use it to find the temperature value. We can use GeoGebra to find the z-score and the corresponding temperature value as follows:

Click on the "Functions" icon and select "InvNorm" function.

Enter the percentile value, which is 0.82 for the 82nd percentile.

Enter the mean and standard deviation values, which are 0 and 1 for this problem.

Click on the "Evaluate" button to find the z-score.

The resulting z-score is 0.934, rounded to 3 decimal places.

This means that the temperature reading separating the bottom 82% from the top 18% is 0 + (0.934)(1.00) = 0.934°C above freezing.

Rounded to the nearest 1000th, this value is 0.934°C.

Therefore, P32, the temperature reading separating the bottom 82% from the top 18%, is approximately 0.934°C.

Explanation: