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Nimfa-mama [501]
3 years ago
15

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.
Mathematics
2 answers:
Oduvanchick [21]3 years ago
8 0

Answer:

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

Step-by-step explanation:

zimovet [89]3 years ago
6 0

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,

E=\frac{s\times z}{\sqrt{n}}

Substitute the value in the formula,

3=\frac{12\times 1.96}{\sqrt{n}}

3=\frac{23.52}{\sqrt{n}}

\sqrt{n}=\frac{23.52}{3}

\sqrt{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.

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