Hershey Kisses Based on Data Set 38 “Candies” in Appendix B, weig...

6. Normal Distribution and Continuous Random Variables

Standard Normal Distribution

Statistics

6. Normal Distribution and Continuous Random Variables

Standard Normal Distribution

1:18 minutes

Problem 6.2.2d

Textbook Question

Hershey Kisses Based on Data Set 38 “Candies” in Appendix B, weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g

d. What is the value of the variance?

Verified step by step guidance

Understand the relationship between standard deviation and variance. Variance is the square of the standard deviation. Mathematically, this is expressed as \( \text{Variance} = (\text{Standard Deviation})^2 \).

Identify the given standard deviation from the problem. Here, the standard deviation is \( 0.1039 \) grams.

Substitute the given standard deviation into the formula for variance: \( \text{Variance} = (0.1039)^2 \).

Perform the squaring operation to calculate the variance. This involves multiplying \( 0.1039 \) by itself.

The result of the squaring operation will give you the variance, which represents the spread of the data in squared units (grams squared).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Variance

Variance is a statistical measure that represents the degree of spread or dispersion of a set of values. It quantifies how much the individual data points differ from the mean of the dataset. In the context of a normal distribution, variance is calculated as the square of the standard deviation, providing insight into the variability of the weights of Hershey Kisses.

Standard Deviation

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It indicates how much individual data points deviate from the mean. A low standard deviation means that the data points tend to be close to the mean, while a high standard deviation indicates a wider spread of values. In this case, the standard deviation of 0.1039 g is crucial for calculating the variance.

Normal Distribution

Normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. It is characterized by its bell-shaped curve and is defined by two parameters: the mean and the standard deviation. Understanding that the weights of Hershey Kisses follow a normal distribution helps in applying statistical methods to analyze their variance.

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Hershey Kisses Based on Data Set 38 “Candies” in Appendix B, weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 gd. What is the value of the variance?