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.

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 of the data set can then be calculated as :

    =

    = 38.88

The standard deviation is calculated by the formula:

   =

   =  3.61

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

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.

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step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .