Computers from a particular company are found to last on average for 24 months without any hardware malfunction with a standard deviation of 2 months. At least 100 ___ % of observations lie between 22 and 26 months?

Question

Mathematics

Yandel Fleming

24 July, 21:15

Computers from a particular company are found to last on average for 24 months without any hardware malfunction with a standard deviation of 2 months. At least 100 ___ % of observations lie between 22 and 26 months?

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Answers (1)

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Karter Owen · Answer 1

At least 68% of observations lie between 22 and 26 months.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 24

Standard deviation = 2

22 = 24 - 2

22 is one standard deviation below the mean

26 = 24 + 2

26 is one standard deviation above the mean.

So, by the empirical rule, at least 68% of observations lie between 22 and 26 months.