Question

The Normal Distribution, also called the Gaussian Distribution, is a representation of the distribution of many different types of data, especially when considering large amounts of data. Some examples of data that are normally distributed are IQ scores, heights, blood pressure measurements and GPAs. The empirical rule, along with the Normal Distribution provides information about the data that is easy to calculate. Follow this link to understand the empirical rule and see an example regarding IQ scores: http://cfcc.edu/faculty/cmoore/Empirical_Rule.htm

For Discussion #2, find an example of data that is normally distributed and cite your source. Do not use IQ scores as an example. Then write a Discussion post with the following information:

·       provide a brief description of the data

·       state the mean

·       state the standard deviation

·       identify the data values that represent the middle 68% of the normal curve

·       identify the data values that represent the middle 95% of the normal curve

·       identify the data values that represent the middle 99.7% of the normal curve

Answer 1

Every normal distribution has a meanand a standard deviation. Given any normal distribution, it will be true that mean = median = mode. The curve is symmetric about the mean, which means that the right and left sides of the curve are identical mirror images of each other. Because the right and left sides are mirror images of each other, 50% of the values are less than the mean and 50% of the values are greater than the mean.

The height of a normal distribution is a maximum at the mean, and the height decreases as one goes from the mean toward the right tail, or as one goes from the mean to the left tail. The total area under the curve is 1, or 100%.

When you are given a normal distribution, with a given mean and standard deviation, you can determine important locations on the bell curve by adding standard deviations to the mean and by subtracting standard deviations from the mean.This is such an important concept that we have a rule of thumb referred to as the Empirical Rule for normal distributions. In all normal distributions, the Empirical Rule tells us that:

1. About 68% of all data values will fall within +/- 1 standard deviation of the mean.
2. About 95% of all data values will fall within +/- 2 standard deviations of the mean.
3. About 99.7% of all data values will fall within +/- 3 standard deviations of the mean.

Keep in mind that when we have skewed data, there are limitations on how we can analyze the data. For example, we can't use the Empirical Rule for data that come from a skewed distribution. A normal distribution is required to use the Empirical Rule.

Example: the heights of the 430 National Basketball Association players were listed on team rosters at the start of the 2005–2006 season. The heights of basketball players have an approximate normal distribution with mean, µ = 79 inches and a standard deviation, σ = 3.89 inches. For each of the following heights, calculate the z-score and interpret it using complete sentences.

1. 77 inches
2. 85 inches
3. If an NBA player reported his height had a z-score of 3.5, would you believe him? Explain your answer.

Answer:  

1. Use the zz-score formula. z=–0.5141z=–0.5141. The height of 77 inches is 0.5141 standard deviations below the mean. An NBA player whose height is 77 inches is shorter than average.
2. Use the zz-score formula. z=1.5424z=1.5424. The height 85 inches is 1.5424 standard deviations above the mean. An NBA player whose height is 85 inches is taller than average.
3. Height =79+3.5(3.89)=90.67=79+3.5(3.89)=90.67 inches, which is over 7.7 feet tall. There are very few NBA players this tall so the answer is no, not likely.