Constructing Normal Quantité Plots. In Exercises, use the given data values to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal quantile plot. Construct the normal quantile plot, then determine whether the data appear to be from a population with a normal distribution.

M&M Weights A sample of weights (g) of M&Ms is obtained from those listed in Data Set 20: 0.864, 0.825, 0.855, 0.942, 0.825, 0.869, 0.912, 0.887, 0.886.

Problem 20BSC

Answer:

Step1 of 3:

We have A sample of weights (g) of M&Ms is obtained from those listed in Data Set 20: 0.864, 0.825, 0.855, 0.942, 0.825, 0.869, 0.912, 0.887, 0.886.

Step2 of 3:

We need to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal quantile plot. Construct the normal quantile plot, then determine whether the data appear to be from a population with a normal distribution.

Step3 of 3:

The given data in Ascending order

0.825 |
0.825 |
0.855 |
0.864 |
0.869 |
0.886 |
0.887 |
0.912 |
0.942 |

Manual Construction of a Normal Quantile Plot:

Step 1. First sort the data by arranging the values in order from lowest to highest.

Step 2. With a sample of size n, each value represents a proportion of 1/n of the sample. Using the known sample size n, identify the areas of 1/2n, 3/2n, 5/2n, 7/2n, and so on. These are the cumulative areas to the left of the corresponding sample values.

Step 3. Use the standard normal distribution (Table A2 or software or a calculator) to find the z scores corresponding to the cumulative left areas found in Step 2. (These are the z scores that are expected from a normally distributed sample.)