Question

A major U.S. automaker has determined that the city mileage for one of its new SUV models is normally distributed with a mean equal to 15.2 mpg. A report issued by the company indicated that 22 percent of the SUV model vehicles will get more than 17 mpg in the city. Given this information, what is the city mileage standard deviation for this SUV model?

Answer 1

Answer:

city mileage standard deviation for this SUV model is 2.34 mpg

Explanation:

given data

mean = 15.2 mpg

company indicated SUV more than 17 mpg  = 22 %

to find out

city mileage standard deviation

solution

we know here that

P(Z > 0.77) is = 0.22

so here z is

z = 0.77

and

we use here z-score formula that is

mean x = z × $\sigma$ + $\mu$   ................1

so

$\sigma$ = ( x - $\mu$ ) ÷ z   ................2

put here value and we get

$\sigma$ = $\frac{17-15.2}{0.77}$  

$\sigma$ = 2.34

so city mileage standard deviation for this SUV model is 2.34 mpg