College

Test Scores: Use the Empirical Rule to answer the following questions.

a. The mean is 62.
b. The standard deviation is _____.

c. What percentage of the test scores are between 58 and 66?
d. What percentage of the test scores are between 54 and 70?
e. What percentage of the test scores are between 50 and 74?
f. What percentage of the test scores are between 62 and 66?
g. What percentage of the test scores are less than 62?
h. What percentage of the test scores are less than 66?

Answer :

Answer:

• B. 4

,

• C. 68.269%

,

• D. 95.45%

,

• E. 99.73%

,

• F. 34.134%

,

• H. 84.134%

Explanation:

The empirical rule tells us that:

• Around 68% of scores are within 2 standard deviations of the mean,

,

• Around 95% of scores are within 4 standard deviations of the mean,

,

• Around 99.7% of scores are within 6 standard deviations of the mean.

Part B

[tex]\begin{gathered} \sigma=62-58=66-62 \\ \sigma=4 \end{gathered}[/tex]

Part C: Between 58 and 66

[tex]\begin{gathered} P(\frac{58-62}{4}Part D: Between 54 and 70.[tex]\begin{gathered} P(\frac{54-62}{4}Part E: Between 50 and 74.[tex]\begin{gathered} P(\frac{50-62}{4}Part F: Between 62 and 66.[tex]\begin{gathered} P(\frac{62-62}{4}Part G: Less than 62.[tex]\begin{gathered} P(x<\frac{62-62}{4}) \\ =P(x<0) \\ =0.5 \\ =50\% \end{gathered}[/tex]

Part H: Less than 66.

[tex]\begin{gathered} P(x<\frac{66-62}{4}) \\ =P(x<\frac{4}{4})=P(x<1) \\ =0.84134 \\ =84.134\% \end{gathered}[/tex]

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