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svetlana [45]
3 years ago
12

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
Mathematics
1 answer:
anastassius [24]3 years ago
3 0

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.

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