# Normal Distribution and Standard Deviation Worksheets

What is Normal Distribution and Standard Deviation? The normal distribution is the statistical phenomenon that tells us how the values are distributed over a dataset. It is a symmetric distribution that reflects most of the values collected around the central peak and other values taper away from the mean in both directions. Like probability distribution, the parameters of the normal distribution determine the probabilities and shape. The normal distribution uses two parameters that define its shape and probabilities, namely, mean and standard deviation. Mean is defined as the central tendency of the distribution. Most of the probability values are collected around the mean. Standard deviation is the statistical measure that calculates the dispersion of the dataset in relation to the square root of its variance. It calculates the variation or deviation of each point from the mean value. If the dataset values are further away from the mean value, the higher is the standard deviation; thus, the dataset is more dispersed.

• ### Basic Lesson

Guides students solving equations that involve an Normal Distribution & Standard Deviation. Demonstrates answer checking. Example: At the New Age Information Corporation, the ages of all new employees hired during the last 5 years are normally distributed. Within this curve, 95.4% of the ages, centered about the mean, are between 24.6 and 37.4 years. Find the mean age and the standard deviation of the data.

• ### Intermediate Lesson

Demonstrates how to solve more difficult problems. Example: Find the percentage of the normally distributed data that lies within 2 standard deviations of the mean. Solution: percentages from -2 to +2 standard deviations.

• ### Independent Practice 1

A really great activity for allowing students to understand the concept of the Normal Distribution and Standard Deviation. Battery lifetime is normally distributed for large samples. The mean lifetime is 500 days and the standard deviation is 61 days. To the nearest percent, what percent of batteries have lifetimes longer than 561 days?

• ### Independent Practice 2

Students explore the Normal Distribution and Standard Deviation in assorted problems. The answers can be found below. A group of 488 students has a mean age of 18.6 years with a standard deviation of 1.2 years. The ages are normally distributed. How many students are younger than 18.9 years? Express answer to the nearest student?

• ### Independent Practice 3

Students are provided with problems to achieve the concepts of Normal Distribution and Standard Deviation. A group of 422 students has a mean age of 20.6 years with a standard deviation of 0.6 years. The ages are normally distributed. How many students are younger than 20.9 years? Express answer to the nearest student?

• ### Independent Practice 4

Example: A group of 964 students has a mean age of 14.2 years with a standard deviation of 0.4 years. The ages are normally distributed. How many students are younger than 14.4 years? Express answer to the nearest student?

• ### Homework

Sample: The amount of time that Carlos plays video games in any given week is normally distributed. If Carlos plays video games an average of 15 hours per week, with a standard deviation of 3 hours, what is the probability of Carlos playing video games between 15 and 18 hours a week?

• ### Quiz

Nancy's scores in Chemistry this semester were rather inconsistent: 200, 115, 105, 95, 195, 200. For this population, how many scores are within one standard deviation of the mean?