A new gas and electricpowered hybrid car has recently hit th

A new gas- and electric-powered 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.

a. The car travels more than 70 miles per gallon.

b. The car travels less than 60 miles per gallon.

c. The car travels between 55 and 70 miles per gallon.

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    70      
u = mean =    65      
          
s = standard deviation =    4      
          
Thus,          
          
z = (x - u) / s =    1.25      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.25   ) =    0.105649774 [ANSWER]

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b)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    60      
u = mean =    65      
          
s = standard deviation =    4      
          
Thus,          
          
z = (x - u) / s =    -1.25      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.25   ) =    0.105649774 [   ANSWER]

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c)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    55      
x2 = upper bound =    70      
u = mean =    65      
          
s = standard deviation =    4      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -2.5      
z2 = upper z score = (x2 - u) / s =    1.25      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.006209665      
P(z < z2) =    0.894350226      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.888140561   [ANSWER]