Normal Distribution and Zscore Normal Curve Has a

Normal Distribution and Z-score

Normal Curve • Has a single peak at the center. • Unimodal. • Mean, median and the mode are equal and located in the center of the curve. • Symmetrical about the mean. • Somewhat bell shaped. • Distributions with such characteristics are frequently considered to be normal distribution. • The total area under is curve is equal to 1.

Normal distribution are completely described by the mean and standard deviation. The 68 -95 -99. 7 rule states that, in a normal distribution approximately 68% of the data lies within one standard deviation of the mean, 95% of the data lies within two standard deviation of the mean, and 99. 7% of the data lies within three standard deviation of the mean.

Z-score

Z-table The z-table gives the proportion less than or equal to a z-score, the proportion must be subtracted from 1 to find the proportion greater than or equal to the z-score In statistics, when talking about a percent of a data set, it is customary to use the word proportion.

Example 1) If X is distributed normally with mean of 100 and standard deviation of 50, suppose the value of X is 250. What is the proportion of the distribution that is less than that z-score?

1) The weekly incomes of shift foremen in the glass industry are normally distributed with a mean of $1, 000 and standard deviation of $100. What proportion of incomes is greater than $1, 100 per week?