Question

Use the given data values​ (a sample of female arm circumferences in​ centimeters) 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.

40.3

34.8

31.8

38.2

44.2



List the z scores for the normal quantile plot.

Answer 1

Answer:

Normal Quantile Plot

Step-by-step explanation:

We are given the following in the question:

40.3 , 34.8 , 31.8 , 38.2 , 44.2

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$  

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.  

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$\mu =\displaystyle\frac{189.3}{5} = 37.86$

Sum of squares of differences = 92.352

$\sigma = \sqrt{\dfrac{92.352}{4}} =$

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

$x = 40.3\Rightarrow z = \dfrac{40.3-37.86}{4.8049} = 0.50\\\\x = 34.8\Rightarrow z = \dfrac{34.8-37.86}{4.8049} = -0.63\\\\x = 31.8\Rightarrow z = \dfrac{31.8-37.86}{4.8049} = -1.26\\\\x = 38.2\Rightarrow z = \dfrac{38.2-37.86}{4.8049} = 0.07\\\\x = 44.2\Rightarrow z = \dfrac{44.2-37.86}{4.8049} = 1.32$

The attached image shows the normal quantile plot.