Using the Empirical Rule, it is found that:
49.85% of soccer balls from the factory have a pressure between 8.1 and 8.7 PSI.
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The Empirical Rule states that, in a normal distribution:
- The middle 68% of the measures are within 1 standard deviation of the mean.
- Following the same logic, 95% is within 2 standard deviations of the mean, and 99.7% within 3.
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- In this question, the mean is of 8.7 PSI and the standard deviation is of 0.2 PSI.
- 8.1 = 8.7 - 3(0.2), thus, 8.1 is 3 standard deviations below the mean.
- The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.
- 99.7% of the 50% of the measures below the mean are between 8.1 and 8.7 PSI, thus, the percentage is:
[tex]P = 0.997(50) = 49.85\%[/tex]
49.85% of soccer balls from the factory have a pressure between 8.1 and 8.7 PSI.
A similar problem is given at https://brainly.com/question/15967965
