Question

A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 50 miles and a standard deviation of 8 miles. Find the z-score, to two decimal places and probability, two four decimals, of the following events: A. The car travels more than 53 miles per gallon. ZZ = PP = B. The car travels less than 42 miles per gallon. ZZ = PP = C. The car travels between 44 and 55 miles per gallon. Z1Z1 = Z2Z2 = PP =

Answer 1

Explanation:

Since the distance travelled on 1 gallon of fuel is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = the distance travelled.

µ = mean distance

σ = standard deviation

From the information given,

µ = 50 miles

σ = 8 miles

A) P(x > 53) = 1 - P(x ≤ 53)

For x = 53,

z = (53 - 50)/8 = 0.38

Looking at the normal distribution table, the probability value corresponding to the z score is 0.648

B) P(x < 42)

For x = 42

z = (42 - 50)/8 = - 1

Looking at the normal distribution table, the probability value corresponding to the z score is 0.1587

C) P(44 ≤ x ≤ 53)

For x = 44

z = (44 - 50)/8 = - 0.75

Looking at the normal distribution table, the probability value corresponding to the z score is 0.2266

For x = 55,

z = (55 - 50)/8 = 0.63

Looking at the normal distribution table, the probability value corresponding to the z score is 0.7357

Therefore,

P(44 ≤ x ≤ 53) = 0.7357 - 0.2266 = 0.5091