A sample of 49 observations is taken from a normal population with a standard deviation of 10. the sample mean is 55. determine
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Answer:
At least 75% of these commuting times are between 30 and 110 minutes
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
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 .
In this question:
Mean of 70 minutes, standard deviation of 20 minutes.
Since nothing is known about the distribution, we use Chebyshev's Theorem.
What percentage of these commuting times are between 30 and 110 minutes
30 = 70 - 2*20
110 = 70 + 2*20
THis means that 30 and 110 minutes is within 2 standard deviations of the mean, which means that at least 75% of these commuting times are between 30 and 110 minutes