A sample of wires coming off the production line was tested for tensile strength. The statistical results (in PSI) were the following: Arithmetic mean 500 Median 500 Mode 500 Standard deviation 40 Quartile deviation 25 Mean deviation 32 Range 240 Sample size 100 According to the Empirical rule, the middle 95% of the wires tested had a tensile strength between approximately what two values

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Mathematics

Frankfurter

20 April, 21:56

A sample of wires coming off the production line was tested for tensile strength. The statistical results (in PSI) were the following: Arithmetic mean 500 Median 500 Mode 500 Standard deviation 40 Quartile deviation 25 Mean deviation 32 Range 240 Sample size 100 According to the Empirical rule, the middle 95% of the wires tested had a tensile strength between approximately what two values

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Simon Schneider · Answer 1

The middle 95% of the wires tested had a tensile strength between approximately 420 PSI and 580 PSI

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 = 500

Standard deviation = 40

According to the Empirical rule, the middle 95% of the wires tested had a tensile strength between approximately what two values

By the empirical rule, within 2 standard deviations of the mean

500 - 2*40 = 420 PSI

500 + 2*40 = 580 PSI

The middle 95% of the wires tested had a tensile strength between approximately 420 PSI and 580 PSI