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Normal Distribution Examples

1- The students of a class have a mean height of 5.5 feet, with a standard deviation of 1.5 feet. What proportion of these students are between 5 and 6 feet tall?

Probability of a (Normal[μ = 5.5 and σ = 1.5]) when the values between 5, 6 is 0.261 = 26.1%

So 26.1% of the students are between 5 and 6 feet.

2- People's monthly utility bills in Gainesville are normally distributed with a mean of 125$ and a standard deviation of 25$. In a complex of 120 apartments, how many would we expect to have a bill that is 100$ or less?

Probability of a (Normal[μ = 125$ and σ = 25$]) when the values less than 100$ is 0.159 = 15.9%

So 15.9% of the apartments have a bill of less than 100$. In this complex, there are 120 apartments so 0.159 * 120 = 19 apartments have a bill less than 100$.

You can use this Normal Distribution Calculator to answer the questions.

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