(2) The highway miles per gallon rating of a certain model of truck is designed
ID: 3358632 • Letter: #
Question
(2) The highway miles per gallon rating of a certain model of truck is designed to be about 31 miles per gallon(mpg). The fuel efficiency that a driver obtains on an individual tank of gasoline naturally varies from tankful to tankful. Suppose the distribution of mpg calculations per tank is Normal and has a mean of 31 mpg and a standard deviation of 3 mpg. mpg or more onn tanks of gas? (b) What should the sample size be so that at least 95% of the sample means are within 0.8 mpg of the population mean?Explanation / Answer
a) Formula: Z = (X - mean)/(SD/sqrt(N))
P(X_bar >= 31.6) = P(Z > (31.6-31)/(3/sqrt(16))) = P(Z > 0.8) = 1 - P(Z < 0.8) = 0.2119
b) Margin of Error, E = 0.8
E = zcrit * SD/sqrt(N)
0.8 = 1.96 * 3/sqrt(N)
N = 54.0225 = 55
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