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

1:09 minutes

Problem 6.R.5b

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.

b. What is the value of the median?

Verified step by step guidance

Recognize that the problem involves a normal distribution, which is symmetric about its mean.

Understand that for a normal distribution, the mean, median, and mode are all equal because of the symmetry of the distribution.

Identify the given mean of the distribution, which is 3037.1 g.

Conclude that since the mean and median are the same for a normal distribution, the median is also 3037.1 g.

State that no further calculations are needed because the median is directly equal to the mean in this case.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Was this helpful?

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 and Median

The mean is the average of a data set, calculated by summing all values and dividing by the number of values. The median, on the other hand, is the middle value when the data set is ordered. In a normal distribution, the mean and median are the same, making it straightforward to determine the median when the mean is known.

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 the spread of birth weights around the mean.

Watch next

Master Finding Standard Normal Probabilities using z-Table with a bite sized video explanation from Patrick

Start learning

����app

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.b. What is the value of the median?