Toepassingen van de normale verdeling

The normal distribution is widely applicable to many problems in real life.

For example, the statistics of human height are used to decide the door height that allows the majority of the people to walk through without striking their heads.

Let's assume that humans have a mean height of 1.7 meters with a standard deviation of 0.06 meters.

The shaded region in the normal distribution represents humans who are 1.9 meters or less.

First, convert the random variable in the X axis into z scores to obtain a standard normal distribution.

A height of 1.9 meters corresponds to a z score of 3.33. The corresponding probability is looked up in the z score table.

The probability is 0.9996, which tells us that 99.96 percent of people can walk through a door 1.9 meters tall.

Similarly, we can calculate the door height that would allow at least 85% of people to pass through without bending.

From the z table, note the value of the z score for a probability of 0.85.

With this z score, the required door height is calculated.