A new car that is a gas- and electric-powered hybrid has recently hit the market
ID: 3152035 • Letter: A
Question
A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 50 miles and a standard deviation of 8 miles. Find the probability of the following events A. The car travels more than 55 miles per gallon Probability = .2676 B. The car travels less than 43 miles per gallon Probability = .1922 C. The car travels between 45 and 55 miles per gallon Probability = -73237-26763 than 55 miles per gallon Probability -73237-26763Explanation / Answer
A)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 55
u = mean = 50
s = standard deviation = 8
Thus,
z = (x - u) / s = 0.625
Thus, using a table/technology, the right tailed area of this is
P(z > 0.625 ) = 0.265985529 [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 = 43
u = mean = 50
s = standard deviation = 8
Thus,
z = (x - u) / s = -0.875
Thus, using a table/technology, the left tailed area of this is
P(z < -0.875 ) = 0.190786953 [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 = 45
x2 = upper bound = 55
u = mean = 50
s = standard deviation = 8
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -0.625
z2 = upper z score = (x2 - u) / s = 0.625
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.265985529
P(z < z2) = 0.734014471
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.468028942 [ANSWER]
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