The length of time required for an automobile driver to respond to a particular

Question

The length of time required for an automobile driver to respond to a particular emergency situation was recorded for n = 10 drivers. The times (in seconds) were 0.6, 0.7, 1.2, 0.7, 0.7, 0.9, 0.6, 0.7, 0.6, 0.9.

(a) Scan the data and use the range approximation to find an approximate value for s. Use this value to check your calculations in part (b). s sec

(b) Calculate the sample mean x and the standard deviation s. (Round your standard deviation to three decimal places.) x = sec s = sec Compare with part

(a). The standard deviations from part (a) and part (b) cannot be compared because they were found using different methods. The standard deviations from part (a) and part (b) are very close. The standard deviation from part (a) is much smaller than the standard deviation in part (b). The standard deviation from part

(a) is much larger than the standard deviation in part (b).

Explanation / Answer

A) s =(max - min)/4

= (1.2 - 0 6) / 4 = 0.6 / 4 = 0.15

B) sample mean = (0.6 + 0.7 + 1.2 + 0.7 + 0.7 + 0.9 + 0.6 + 0.7 + 0.6 + 0.9) / 10 =0.76

Variance = ((0.6 - 0.76)2 + (0.7 - 0.76)2 + (1.2 - 0.76)2 + (0.7 - 0.76)2 + (0.7 - 0.76)2 + (0.9 - 0.76)2 + (0.6 - 0.76)2 + (0.7 - 0.76)2 + (0.6 - 0.76)2 + (0.9 - 0.76)2) / 9 = 0.036

Standard deviation = sqrt(0.036) = 0.19

The standard deviations from part (a) and part(b) are very close.

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