Exercise 3. Approximations

Notice that the approximation calculated in the second question is very close to the exact calculation in the first question. The normal distribution was a useful approximation for this case.

However, the approximation is not always useful. An example is for the more extreme values, often called the "tails" of the distribution. Let's look at an example. We can compute the proportion of heights between 79 and 81.

library(dslabs)
data(heights)
x <- heights$height[heights$sex == "Male"]
mean(x > 79 & x <= 81)

Use normal approximation to estimate the proportion of heights between 79 and 81 inches and save it in an object called approx.
Report how many times bigger the actual proportion is compared to the approximation.