Question

To determine the mean speed of vehicles driven on interstate I-80, vehicles are randomly observed and their speeds (in mph) are recorded with a radar gun. In previous samplings the sample standard deviation has been 6.0 mph. How many vehicles need to be measured and recorded to achieve a 95% margin of error of at most 0.9 mph?

Answer 1

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Solution

standard deviation =s = 6mph.

Margin of error = E = 0.9mph.

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z/2* / E] 2

n = ( 1.96* 6 / 0.9 )2

n =170.7377

Sample size = n =171