A new car that is a gas and electricpowered hybrid has recen

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 55 miles and a standard deviation of 8 miles. Find the probability of the following events: The car travels more than 59 miles per gallon. The car travels less than 47 miles per gallon. The car travels between 50 and 63 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]