Vehicle speeds at a certain highway location are believed to have approximately

Question

Vehicle speeds at a certain highway location are believed to have approximately a normal distribution with mean (U symbol) of 60mph and standard deviation (O symbol) of 6 mph. THe speeds for a randomly selected sample of n=36 vehicles will be recorded. a) Give numerical values for the mean and standard deviation of the sampling distribution of possible sample means for randomly selected samples of n=36 from the population of vehicle speeds. b) use the empirical rule to find values that fill in the blanks in the following sentence: For a random sample of n=36 vehicles, there is about a 95% chance that the mean vehicle speed in the sample will be between _____ and ___ mph. c) sample speeds for a random sample of 36 vehicles are measured at this location , and the sample mean is 66 mph. Given the answer to part (B), explain whether this result is consistent with the belief that the mean speed at this location is (U symbol)= 60 mph.

Explanation / Answer

a)

By central limit theorem, it has the same mean,

u(X) = 60 mph [ANSWER]

and a reduced standard error,

sigma(X) = sigma/sqrt(n) = 6/sqrt(36) = 1 [ANSWER]

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b)

By empirical rule, it is 2 standard deviations below and above the mean, so it is between

60 - 2*1 and 60 + 2*1

or

58 and 62 [ANSWER]

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C)

As 66 is outside the interval (58, 62), then getting 66 as sample mean is not consistent with the belief that the mean speed at this location is u = 60 mph.

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