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

1:19 minutes

Problem 6.2.2b

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

b. What is the value of the median?

Verified step by step guidance

Step 1: Understand the relationship between the mean and the median in a normal distribution. In a normal distribution, the mean, median, and mode are all equal because the distribution is symmetric.

Step 2: Identify the given parameters of the normal distribution. The problem states that the mean weight of Hershey Kisses is 4.5338 g and the standard deviation is 0.1039 g.

Step 3: Recall that the median in a normal distribution is equal to the mean. This is a property of the normal distribution due to its symmetry.

Step 4: Conclude that the median weight of Hershey Kisses is the same as the mean weight, which is 4.5338 g.

Step 5: No further calculations are needed because the median is directly determined by the mean in a normal distribution.

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Key Concepts

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

Normal Distribution

Normal distribution is a probability distribution that is symmetric about the mean, indicating that data near the mean are more frequent in occurrence than data far from the mean. In a normal distribution, the mean, median, and mode are all equal, which simplifies the calculation of the median when the distribution is known.

Mean

The mean is the average of a set of values, calculated by summing all the values and dividing by the number of values. In the context of a normal distribution, the mean serves as the central point around which the data is distributed, and it is crucial for understanding the overall distribution of the dataset.

Median

The median is the middle value of a dataset when it is ordered from least to greatest. For a normal distribution, the median is equal to the mean, making it straightforward to determine in this case. It represents the point at which half of the data points fall below and half fall above.

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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 gb. What is the value of the median?