6.12 : Applications of Normal Distribution

The normal distribution is a useful statistical tool. One of its practical applications is determining the door height after considering the normal distribution of heights of persons, such that many can pass through it easily without striking their heads. The normal distribution can also determine the probability of a person having a height less than a specific height.

The heights of 15 to 18-year-old males from Chile from 1984 to 1985 followed a normal distribution. The mean height is 172.36 cm, and the standard deviation of 6.34 cm. This information can be used to find the probability of males from Chile having a height of less than 162.85 cm.

Begin by finding the z score for the height of 162.85 cm. After using the formula for the z score, the value is found to be -1.5. From the table for negative z scores, the cumulative area under the curve (from the left of the standard normal distribution) or the probability is found to be 0.0668. Converting this value to a percentage gives 6.68%. It can be concluded that there is a 6.68% probability of males among 15 to 18-year-old males that have a height below 162.85 cm.