Question

Assume that the readings on thermometers are normally distributed with a mean of 0 and a standard deviation of 1.00.

A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to

Upper P 83 (83 percentile). This is the temperature reading separating the bottom 83 % from the top 17 %.

Please give me explicit instructions step by step. I read others here and need extreme detail on how to do this. Thank you.

Answer 1

It is given that, readings on thermometer follows Normal distribution with mean 0 and standard deviation of 1. Let the reading of thermometer be denoted by Z. Then, Z~N(0,1).

We have to find the P83 i.e. value of Z-score corresponding to 83th percentile which can be shown as below:

Thus, from the above diagram, it is clear that the value of upper P83 (83rd percentile) i.e. the value of temperature reading separating the bottom 83 % from the top 17 % is equal to 0.954.