Question

Shoe sizes for men in the United States are known to follow a normal distribution. If you calculated the z-score of a man's shoe size and found the z-score to be 2.9, what would you conclude about his shoe size

Answer 1

Answer:

This value means that his shoe size is 2.9 deviations above the population mean.

And we can find the approximate percentile for his measure like this:

$P(Z$

This correspond to the 99.8 percentile, so then his shoe size is 99.8% above all the shoe sizes.

Step-by-step 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 shoe size of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,\sigma)$  

Where $\mu$ represent the mean and $\sigma$ the population standard deviation.

For this case we know that a man obtain a z score of z=2.9

This value means that his shoe size is 2.9 deviations above the population mean.

And we can find the approximate percentile for his measure like this:

$P(Z$

This correspond to the 99.8 percentile, so then his shoe size is 99.8% above all the shoe sizes.