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The distribution of scores on a mathematics placement exam is close tonormal. Where the mean is x¯ = 70 and the standard deviation is σ = 10. Use the 68-95-99.7% Rule to find the percent of scores between 40 and 60.

Question

The distribution of scores on a mathematics placement exam is close to
normal. Where the mean is x¯ = 70 and the standard deviation is σ = 10. Use the 68-95-99.7% Rule to find the percent of scores between 40 and 60.

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Step 1

68-95-99.7-rule:

Let X be an observation from a normal distribution, having mean µ and standard deviation σ, then according to the 68-95-99.7-rule, approximately 68.2%,95% and 99.7% of the values lie within one, two and three standard deviations of the mean respectively. That is,

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Step 2

Finding the percentage of scores between 40 and 60:

It is given that the scores on the mathematics exam is approximately normally distributed with mean 70 and standard deviation 10. That is, x-bar = µ =70 and σ = 10. The following figure represents the 68-95-99.7-rule.

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Step 3

Substituting the values µ =70 and &si...

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