Question

The accompanying data represent the miles per gallon of a random sample of cars with a​ three-cylinder, 1.0 liter engine. ​(a) compute the​ z-score corresponding to the individual who obtained 42.342.3 miles per gallon. interpret this result.

Answer 1

Answer:

The z- score corresponding to the individual who obtained 42.3 miles per gallon is 0.9474 which indicates that it is 0.9474 standard deviations below the mean.

Step-by-step explanation:

From the data set attached below;

Let consider that the random  variable X as the miles per gallon driven by cars with a three cylinders, 1.0 liter engine.

The mean $\mu$ of the data set can then be calculated as :

$\mu = \dfrac{1}{n} \sum\limits^n_{ i=1} x_i$

    = $\dfrac{31.5+34.2+34.7+...+42.5+43.4+49.3}{24}$

    = 38.88

The standard deviation is calculated by the formula:

$\sigma = \sqrt{\dfrac{1}{n-1} \sum\limits^n_{ i=1} (x_i- \mu)^2}$

   = $\sqrt{\dfrac{(31.5-38.88)^2+...+(49.3-38.88)^2}{24-1}}$

   =  3.61

The z score corresponding to the value x = 42.3 can be calculated as:

$z = \dfrac{x-\mu}{\sigma}$

$z = \dfrac{42.3-38.88}{3.61}$

z = 0.9474

The z- score corresponding to the individual who obtained 42.3 miles per gallon is 0.9474 which indicates that it is 0.9474 standard deviations below the mean.