Question

How many commuters must be randomly selected to estimate the mean driving time of chicago commuters? we want 95% confidence that the samoke mean is within 4 minutes of the population mean, and the population standard deviation is known to be 10 minutes?

Answer 1

Margin of error is calculated using the following formula:

Margin error = Z-value*SD/Sqrt (N)

Where: Z -value at 95% confidence = 1.96; SD = Standard deviation = 10 minutes; N = Sample size; Margin error = 4 minutes

Substituting;
4 = 1.96*10/Sqrt (N)
Sqrt (N) = (1.96*10)/4 = 4.9
N = 4.9^2 = 24.01 ≈ 25

Therefore, 25 commuters will be selected at random to yield these results.