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

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.

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 = (1)/(n) \sum\limits^n_( i=1) x_i`

=
`(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{(1)/(n-1) \sum\limits^n_( i=1) (x_i- \mu)^2}`

=
`\sqrt{((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 = (x-\mu)/(\sigma)`

`z = (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.