The average gas mileage of a certain model car is 28 miles p

The average gas mileage of a certain model car is 28 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 1.7, find the probability that a car has a gas mileage of between 27.8 and 28.3 miles per gallon?

The average hourly wage of workers at a fast food restaurant is $6.50/hr with a standard deviation of $0.45. Assume that the distribution is normally distributed. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75?

If the scores for a test have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall below 50?

Solution

1. The average gas mileage of a certain model car is 28 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 1.7, find the probability that a car has a gas mileage of between 27.8 and 28.3 miles per gallon?

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    27.8      
x2 = upper bound =    28.3      
u = mean =    28      
          
s = standard deviation =    1.7      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -0.117647059      
z2 = upper z score = (x2 - u) / s =    0.176470588      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.453173658      
P(z < z2) =    0.570037873      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.116864215   [ANSWER]  

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