Question

CITA collects data on cell phones and publishes the results in Semi-annual Wireless Survey. A sample of 15 monthly cell-phone bills gave the following data.

Part (a): Use Table III in Appendix A to construct a normal probability plot of the given data.

Part (b): Use part (a) to identify any outliers.

Part (c): Use part (a) to access the normality of the variable under consideration.

Short answer

Part (a): The required normal probability plot is given below,

Part (b): There are no outliers for the given data.

Part (c): The monthly cell phone bills follows normal distribution.

Step-by-step solution

Part (a) Step 1. Given information.

Consider the given question,

Part (a) Step 2. Construct a normal probability plot.

Use Table III in Appendix A to construct the normal probability plot for the data on monthly cell phone bills.

A sample of $15$monthly cell phone bills is considered.

From Appendix A, Table III, Normal scores, the z-scores corresponding to the column $n=15$for the data on monthly cell phone bills is tabulated below,

Part (a) Step 3. Plot the points.

Use the z-scores to construct normal probability plot for the given data,

Part (b) Step 1. Identify any outliers.

Consider the normal probability plot from part (a),

From the above probability plot, there are no unusual observations. Thus, it can be concluded that there are no outliers for the given data.

Part (c) Step 1. Access the normality of the variable under consideration.

Consider the normal probability plot from part (a),

From the probability of monthly cell phone bills, it is clear that all the points are close to the line.

Hence, it can be concluded that the monthly cell phone bills follows normal distribution.