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 P25, the 25-percentile. This is the temperature reading separating the bottom 25% from the top 75%. P25 = °C

Answer 1

`X \sim N(0,1)`

Where
`\mu=0` and
`\sigma=1`

So then we can find in the normal standard distribution or in excel a value of Z who accumulates 0.25 of the area below and 0.75 of the area above. We can use the following excel code for example:

="NORM.INV(0.25,0,1)"

And we got = z= -0.674.

So the value of height that separates the bottom 25% of data from the top 75% is -0.674 °C.

Explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the readings at freezing of a population, and for this case we know the distribution for X is given by:

`X \sim N(0,1)`

Where
`\mu=0` and
`\sigma=1`

So then we can find in the normal standard distribution or in excel a value of Z who accumulates 0.25 of the area below and 0.75 of the area above. We can use the following excel code for example:

="NORM.INV(0.25,0,1)"

And we got = z= -0.674.

So the value of height that separates the bottom 25% of data from the top 75% is -0.674 °C.