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
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
Calculate the amount that would be one standard deviation below the mean, and save it to the variable
Print the values of
one_below to the terminal.
2000 students took the exam. How many would you expect to have scores within the range of
Save your response to the variable
one_std and print it to the terminal.