Question

A car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 litre of fuel is normally distributed with a mean of 20 km and a standard deviation of 6 km. Find the probability (to 3 decimal places) that the car travels between 15 and 28 km on 1 litre of fuel.

Answer 1

0.70631

Explanation:

Given that :

Mean (m) = 20 km

Standard deviation (s) = 6 km

Probability that car travels between 15 and 28 km

Using the relation to obtain the standardized score (Z) :

p(x < 15)

Z = (x - m) / s

Z = (15 - 20) / 6

= - 0.8333

p(Z < - 0.833) = 0.20242 ( Z probability calculator)

(x < 28)

Z = (x - m) / s

Z = (28 - 20) / 6

= 1.333

p(Z < 1.333) = 0.90873 ( Z probability calculator)

0.90873 - 0.20242 = 0.70631