A set of exam scores is normally distributed with a mean = 80 and standard deviation...

A set of exam scores is normally distributed with a mean = 80 and standard deviation = 8.
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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Expert Solution

Given in the question
P(X < x) = 0.68

This implies that
P(Z < 0.4676987991145084) = 0.68
z score value corresponding to 68% = 0.4676987991145084

With the help of formula for z, we can say that

b) Given in the question
P(X < x) = 0.95

This implies that
P(Z < 1.6448536269514722) = 0.95
z score value corresponding to 95% = 1.6448536269514722

With the help of formula for z, we can say that

c) Given in the question
P(X < x) = 0.997

This implies that
P(Z < 2.7477813854449926) = 0.997
z score value corresponding to 99.7% = 2.7477813854449926

With the help of formula for z, we can say that

PS: you have to refer z score table to find the final probabilities.

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orchestra answered 2 years ago

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