3.b. A new gas-electric hybrid car has recently hit the market. The distance traveled on
1 gallon of fuel is normally distributed with a mean of 65 miles and a standard
deviation of 4 miles. Find the probability of the following events. (show the
concerned region by z curve)
1. The car travels more than 70 miles per gallon
2. The car travels less than 60 miles per gallon
3. The car travels between 55 and 70 miles per gallon.
(5 Marks)
Answers
Given : A new gas-electric hybrid car has recently hit the market.
The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles.
To Find : the probability of the following events
1. The car travels more than 70 miles per gallon
2. The car travels less than 60 miles per gallon
3. The car travels between 55 and 70 miles per gallon.
Solution:
z score = ( Value - Mean ) / SD
Mean = 65
SD = 4
The car travels more than 70 miles per gallon
Value = 70
z score = ( 70 - 65)/4 = 1.25
=> 0.8944 is less than for z score 1.25
=> Probability The car travels more than 70 miles per gallon = 1 - 0.8944
= 0.1056
2. The car travels less than 60 miles per gallon
Value = 70
z score = ( 60 - 65)/4 = -1.25
=> 0.1056 is less than for z score -1.25
=> Probability The car travels less than 60 miles per gallon = 0.1056
The car travels between 55 and 70 miles per gallon.
0.8944 is less than for z score 1.25 for 70 miles per gallon.
z score = ( 55 - 65)/4 = -2.5
=> 0.0062 is less than for z score -2.5
=> Probability car travels between 55 and 70 miles per gallon.
= 0.8944 - 0.0062
= 0.8882
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