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Scores on a test are normally distributed with a mean of 110 and a standard deviation of 19. What percentage of scores are greater than 167?

A. 0.15%
B. 0.3%
C. 99.7%
D. 99.85%

User Marti
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1 Answer

3 votes

Answer:

B.

Explanation:

Apply the 68-95-99.7 rule

The rule supposed that;

68% of the data in a standard normal distribution falls within 1 standard deviation of the mean.

95% of the data in a standard normal distribution falls within 2 standard deviation of the mean.

99.7% of the data in a standard normal distribution falls within 3 standard deviation of the mean.

Evaluating

Given the mean as 110 and the standard deviation as 19 then;

68% of the scores will be between 110-19=91 & 110+19=129

95% of the scores will be between 110-2(19)= 72 & 110+2(19)=148

99.7% of the scores will be between 110-3(19)= 53 & 110 +3(19)= 167

Analysis

68% of the scores will lie between 91 and 129 points.

95% of the scores will lie between 72 and 148 points

99.7% of the scores will lie between 53 and 167 points.

User Reed Hedges
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