Question

he file Utility contains the electricity costs, in dollars, during July of a recent year for a random sample of 50 one-bedroom apartments in a large city: SELF TEST 96 171 202 157 185 90 141 149 206 95 163 150 108 119 183 178 147 116 172 175 123 154 130 151 114 102 153 111 148 128 144 143 187 135 191 197 127 82 213 130 165 168 109 167 166 139 149 137 129 158 Decide whether the data appear to be approximately normally distributed by a. comparing data characteristics to theoretical properties. b. constructing a normal probability plot.

Answer 1

a) Comparing data characteristics:

The normal distribution has a property of mean=median, and is a one-peaked, symmetric graph.

Considering the data given, using R, i have obtained mean, median of the data as well as plotted a histogram of data. Attaching the image of R code and output below.

Mean = 147.06 and median = 148.5, which are not equal but are quite close. The histogram also reflects a one peaked roughly symmetric distribution. Therefore, considering the theoretical qualities, given data can be approximated to normal distribution.

b) Using Normal probability plot. Below you can see that all the points in the normal probability plot lie close on the straight line. Hence the data can be approximated to normal. If the points would have been scattered and not falling on/near the straight line, then the data would not reflect any normality.

Hope this helped. All the best...!