After collecting the speed data in the table below on a highway with a speed limit of 55 mi/h, determine the percent of vehicles exceeding the limit. Also determine the percent of vehicles traveling within 5 mi/h above the speed limit.

Question

What will be an ideal response?

Answer 1

Compute the mean and standard deviation of the data provided:

Mean = 56.1 mi/h

Standard deviation = 5.7 mi/h

Since we are comparing the mean of the data to the speed limit, use Eq. 4.6 to

compute the Z-value

Z = (X – ave)/stdev

Z = (55 – 56.1) / 5.7

= -0.193

Look up this value in Table A.1 to obtain the area under the curve to the left of 55

mi/h = 0.425 or 42.5%. This is the percent of vehicles driving below the speed

limit. Subtract this from 100% to find the percent of vehicles driving above the

speed limit = 100% - 42.5% = 57.5%

Part 2 asks how many vehicles are driving “within 5 mi/h above the speed limit”

or between 55 and 60 mi/h. Given that 42.5% of vehicles are driving below 55

mi/h, use Eq. 4.6 again at 60 mi/h to find the percent of vehicles driving below 60

mi/h.

Z = (X – ave)/stdev

Z = (60 – 56.1) / 5.7

= +0.684

Looking this up in the standard normal distribution table gives 75.2% driving

below 60 mi/h. The percent of vehicles driving below 60 mi/h but above the 55

mi/h speed limit is 75.2% - 42.5% = 32.7%.