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Brrunno [24]
3 years ago
8

the mean of the commute time to work for a resident of a certain city is 28.8 minutes. assume the standard deviation of the comm

ute time is 8.1 minutes. what minimum percentage of the commuters in the city has a commute time within 2 standard deviations of the mean?
Mathematics
1 answer:
hjlf3 years ago
3 0

Answer:

The minimum percentage of the commuters in the city has a commute time within 2 standard deviations of the mean is 75%.

Step-by-step explanation:

We have no information about the shape of the distribution, so we use Chebyshev's Theorem to solve this question.

Chebyshev Theorem

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by 100(1 - \frac{1}{k^{2}}).

Applying the Theorem

The minimum percentage of the commuters in the city has a commute time within 2 standard deviations of the mean is 75%.

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