Describe a real-life set of data that could be described by: X~N(68000, 9000^2). Include units.

Question

Hi, this is a Grade 12 Data Management course about Normal Distirbutions and Z-scores. I need to describe this situation in a sentence or 2, not too long but just say a scenario of this that could happen in real life. The average is 68000 and the standard deviation is 9000. The units can be anything. I also have another one to describe, it is X~N(230, 144) Including units.

Answer 1

$68,000 could be an average annual salary with a standard deviation of $9000 (13% of the mean). This would give an expected salary range of $59,000-$77,000. The normal distribution would show the probability of selecting a randomly selected salary X.

The second example has a standard deviation of 12 (about 5% of the mean) indicating a narrow spread 218-242. This could be the number of miles a car starting with a full tank of fuel could be driven before needing refuelling. The normal distribution would show how likely refuelling would be necessary for a journey of X miles.