Homework for 2.1 Day 1: 41, 43, 45, 47, 49, 51
1) To use the rule to estimate the percent of observations from a Normal Distribution that fall in an interval 2) Use the standard Normal distribution to calculate the proportion of values in a specified interval 3) Use the standard Normal distribution to determine a z-score from a percentile 4) Use Table A to find the percentile of a value from any Normal distribution 5) Make an appropriate graph to determine if a distribution is bell-shaped 6) Use the rule to assess normality of a data set 7) Interpret a normal probability plot
On the board Keep in mind: these are special properties of normal distributions NOT ALL DENSITY CURVES!!!!
Page 114
Z-Scores!! Check out the box on page 115 Now, let’s look up our Table A in the back of the book… These are the values of the z scores, the area under the curve to the left of z Example: Suppose we wanted to find the proportion of observations in a Normal distribution that were more than 1.53 standard deviations above the mean. Ok, so we want to know what proportion of observations in the standard Normal distribution are greater than, z=1.53
Look at the beige box on page 120 Example: In the 2008 Wimbledon tennis tournament, Rafael Nadal averaged 115 MPH on his first serves. Assume that the distribution of his first serve speeds is Normal with a mean of 115 mph, and a standard deviation of 6 mph. About what portion of his speeds would you expect to exceed 120 mph? Conclude: About 20% of Nadal’s first serves will travel more than 120 mph.
What percent of Rafael Nadal’s first serves are between 100 and 110 mph? Conclude: About 20% of Nadal’s first serves will travel between 100 and 110 mph
The heights of three-year old females are approximately Normally distributed with a mean of 94.5 cm and a standard deviation of 4 cm. What is the third quartile of this distribution? Hint: Look at the z-chart in reverse!! Conclude: The third quartile of three-year old females’ heights is cm
1. Plot the data- you can use a dotplot, stemplot, or histogram. See if the shape is a bell 2. Check to see if the data follows the Rule A. Find the mean and standard deviation B. Calculate 1, 2, and 3 standard deviations to the right and left C. Find the percent of the data that lies between those standard deviations
12.9, 13.7, 14.1, 14.2, 14.5, 14.5, 14.6, 14.7, 15.1, 15.2, 15.3, 15.3, 15.3, 15.3, 15.5, 15.6, 15.8, 16.0, 16.0, 16.2, 16.2, 16.3, 16.4, 16.5, 16.6, 16.6, 16.6, 16.8, 17.0, 17.0, 17.2, 17.4, 17.4, 17.9, 18.4
Combined with the graph, and the fact that these numbers are extremely close to our rule, we have good evidence to believe this is a Normal Distribution