Question

A set of exam scores is normally distributed with a mean = 80 and standard deviation = 10.
Use the Empirical Rule to complete the following sentences.

68% of the scores are between _____ and ______.

95% of the scores are between ______ and _______.

99.7% of the scores are between _______ and ________.

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Answer 1

Solution :

Using Empirical rule,

P( - 1< X < + 1) = 68%

P(80 - 1 * 10 < X < 80 + 1 *10) = 68%

P(70 < X < 90) = 68%

68% of the scores are between 70 and 90

P( - 2< X < + 2) = 95%

P(80 - 2 * 10 < X < 80 + 2 * 10) = 95%

P(60 < X < 100) = 95%

95% of the scores are between 60 and 100

P( - 3< X < + 3) = 99.7%

P(80 - 3 * 10 < X < 80 + 3 * 10) = 99.7%

P(50 < X < 110) = 99.7%

99.7% of the scores are between 50 and 110