Birth Weights Based on Data Set 6 “Births” in Appendix B, birth w...

6. Normal Distribution and Continuous Random Variables

Standard Normal Distribution

Statistics

6. Normal Distribution and Continuous Random Variables

Standard Normal Distribution

1:21 minutes

Problem 6.R.5c

Textbook Question

Birth Weights Based on Data Set 6 “Births” in Appendix B, birth weights of girls are normally distributed with a mean of 3037.1 g and a standard deviation of 706.3 g.

c. What is the value of the mode?

Verified step by step guidance

The mode is the value that appears most frequently in a data set. For a normal distribution, the mode is the same as the mean and the median because the distribution is symmetric.

In this problem, the birth weights of girls are described as being normally distributed. This means the mode will coincide with the mean of the distribution.

The mean of the birth weights is given as 3037.1 g. Therefore, the mode is also 3037.1 g.

No further calculations are needed because the mode for a normal distribution is directly equal to the mean.

Thus, the mode of the birth weights is the same as the mean, which is 3037.1 g.

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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 analysis of data sets that follow this pattern.

Mean, Median, and Mode

The mean is the average of a data set, the median is the middle value when the data is ordered, and the mode is the most frequently occurring value. In a normal distribution, these three measures of central tendency coincide, making it easier to identify the central point of the data.

Standard Deviation

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. In the context of normal distribution, it helps to understand how data points are distributed around the mean.

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Birth Weights Based on Data Set 6 “Births” in Appendix B, birth weights of girls are normally distributed with a mean of 3037.1 g and a standard deviation of 706.3 g.c. What is the value of the mode?