Batch of thermometers

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 P₇, the 7-percentile. This is the temperature reading separating the bottom 7% from the top 93%. Round answer to 3 decimal places.

Answer 1

Hi Bailey,

This problem uses the classic equation in elementary statistics:

z=x-mu/sigma where:

z=z-score, described below

x=value you are looking for, 7th percentile temp. in this case

mu=mean

sigma=standard deviation

You were asked to find the 7th-percentile. z-scores come either from z-tables, which you can find by searching "z score table" in a browser, or from statistical software. We'll use tables here. Again, you were given the 7th percentile, which is 0.07, so look in the interior of your z-table for the value closest to 0.07. For my table, this was 0.0694.

Once you have this value, look at the column on the left and the row up top, which gives -1.48.

You are fortunate here to have the standard normal distribution with mean 0 and standard deviation 1, which means you don't need to do any calculation beyond this. To wit:

z=-1.48

x=x, the temp. we are looking for

mu=0

sigma=1

Thus:

-1.48=(x-0)/1

-1.48=x

The 7th percentile is about -1.480 degrees Celsius. I hope this helps.