Question

How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 95% confidence that the sample mean is within 3 minutes of the population mean, and the population standard deviation is known to be 12 minutes.

Answer 1

61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.

Explanation:

Answer 2

61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.

Explanation:

Given : We want 95% confidence that the sample mean is within 3 minutes of the population mean, and the population standard deviation is known to be 12 minutes.

To find : How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters?

Solution :

At 95% confidence the z-value is z=1.96

The sample mean is within 3 minutes of the population mean i.e. margin of error is E=3 minutes

The population standard deviation is s=12 minutes

n is the number of sample

The formula of margin of error is given by,

`E=(s* z)/(√(n))`

Substitute the value in the formula,

`3=(12* 1.96)/(√(n))`

`3=(23.52)/(√(n))`

`√(n)=(23.52)/(3)`

`√(n)=7.84`

Squaring both side,

`n=61.4656`

Therefore, 61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.