The average gas mileage of a certain model car is 28 miles per gallon. If the ga
ID: 3022536 • Letter: T
Question
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?
Explanation / Answer
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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