The miles per gallon for hybrid vehicles on city streets have been determined to be normally distributed with a mean of 33.2 mpg and a variance of 16. Based on this information, the probability that if three randomly selected vehicles are monitored and that two of the three will exceed the 35 mpg is slightly greater than 0.18.

Question

Quizplus · Accepted Answer

Given the mean (μ) = 33.2 mpg and variance (σ^2) = 16, the standard deviation (σ) = √16 = 4 mpg. To find the probability of a single vehicle exceeding 35 mpg, we first calculate the Z-score for 35 mpg, which is (35 - 33.2) / 4 = 0.45. The probability associated with this Z-score can be found using a standard normal distribution table or calculator, which gives a probability of a single vehicle exceeding 35 mpg. However, the question asks for the probability that exactly two out of three vehicles exceed 35 mpg, which involves binomial probability calculations, not directly provided by the information given. The statement's conclusion about the probability being slightly greater than 0.18 without showing these calculations or the exact probability for a single vehicle exceeding 35 mpg is not directly inferable from the given data.

The Miles Per Gallon for Hybrid Vehicles on City Streets