A spot speed study was conducted on a freeway on which the mean speed and standard deviation were found to be 72.4 mi/h and 5.4 mi/h respectively. What is the range of values that would be expected to contain the middle 95% of speeds?
What will be an ideal response?
If it can be assumed that the true mean of the speeds in a section of highway is ?
and the true standard deviation is ?, it can be concluded that all vehicle speeds
will be between (? – Z?) and (? + Z?). For this problem, it is known that:
? = 72.4 mi/h
? = 5.4 mi/h
Z = 1.96 for a 95% confidence level
Therefore, the range of values that would be expected to contain the middle 95%
of speeds will be:
(? – Z?), (? + Z?) = (72.4 – 1.96 × 5.4), (72.4 + 1.96 × 5.4) = (61.8, 83.0).
95% of all vehicle speeds will be between 61.8 and 83.0 mi/h.
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