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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:
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:
Where represent the mean and
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:
This correspond to the 99.8 percentile, so then his shoe size is 99.8% above all the shoe sizes.