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Statistical Distributions with NumPy
Standard Deviations and Normal Distribution, Part II

We know that the standard deviation affects the “shape” of our normal distribution. The last exercise helps to give us a more quantitative understanding of this.

Suppose that we have a normal distribution with a mean of 50 and a standard deviation of 10. When we say “within one standard deviation of the mean”, this is what we are saying mathematically:

lower_bound = mean - std = 50 - 10 = 40 upper_bound = mean + std = 50 + 10 = 60

It turns out that we can expect about 68% of our dataset to be between 40 and 60, for this distribution.

As we saw in the previous exercise, no matter what mean and standard deviation we choose, 68% of our samples will fall between +/- 1 standard deviation of the mean!

In fact, here are a few more helpful rules for normal distributions:

  • 68% of our samples will fall between +/- 1 standard deviation of the mean
  • 95% of our samples will fall between +/- 2 standard deviations of the mean
  • 99.7% of our samples will fall between +/- 3 standard deviations of the mean

Instructions

1.

The average score on the SATs is 1000 and the standard deviation is 100.

Calculate the amount that would be one standard deviation above the mean, and save it to the variable one_above.

2.

Calculate the amount that would be one standard deviation below the mean, and save it to the variable one_below.

3.

Print the values of one_above and one_below to the terminal.

4.

2000 students took the exam. How many would you expect to have scores within the range of one_above and one_below?

Save your response to the variable one_std and print it to the terminal.

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