Chapter 2, Problem T2.11SPT

(a)

To determine

To find: the percentile of the house indicated in red on the dot plot.

Answer to Problem T2.11SPT

65^th percentile

Explanation of Solution

Given:

  

Formula used:

  $\text{percentile=}\frac{\text{number}\text{of data values that are less than the individual's data value}}{\text{total number of data values}}\text{×100\%}$

Calculation:

By seeing the dot plot, it is observed that 26 of the 40 dots to the left of the red dot and therefore 26 of the 40 house in the sample have a price below $234000 which is the certain value associating to the red dot.

The percentile is the number of data values that are less than the individual’s data value divided by the number of data values in total

  $\begin{array}{c}\text{percentile=}\frac{\text{number}\text{of data values that are less than the individual's data value}}{\text{total number of data values}}\text{×100\%}\\ \text{=}\frac{\text{26}}{\text{40}}\text{×100}\\ \text{=65\%}\end{array}$

Therefore the percentile associating with the red dot is the 65^th percentile

(b)

To determine

To Calculate: and interpret the standardized score for the house indicated by the red dot, which sold for $234000

Answer to Problem T2.11SPT

The sold price of $234000 for the house is 0.35 standard deviations above the mean sold price of $203388.

Explanation of Solution

Given:

  $\begin{array}{c}\mu =203388\\ \sigma =87609\\ x=234000\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{c}z=\frac{x-\mu }{\sigma }\\ =\frac{234000-203388}{87609}\\ =0.35\end{array}$

The z-score indicating that the number of standard deviation that a value forms the mean, while a negative z-score means that the value is below the mean and a positive z-score means that the value is above the mean.

The sold price of $234000 for the house is 0.35 standard deviations above the mean sold price of $203388.