Answer:
61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.
Step-by-step 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,
[tex]E=\frac{s\times z}{\sqrt{n}}[/tex]
Substitute the value in the formula,
[tex]3=\frac{12\times 1.96}{\sqrt{n}}[/tex]
[tex]3=\frac{23.52}{\sqrt{n}}[/tex]
[tex]\sqrt{n}=\frac{23.52}{3}[/tex]
[tex]\sqrt{n}=7.84[/tex]
Squaring both side,
[tex]n=61.4656[/tex]
Therefore, 61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.
Answer:
61 commuters must be randomly selected to estimate the mean driving time of Chicago commuters.
Step-by-step explanation:
