A normal distribution has a mean of 15 and a standard deviation of 4 . Use...

A normal distribution has a mean of 15 and a standard deviation of 4 . Use the? 68-95-99.7 rule to find the percentage of values in the distribution between 15 and 23 .

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Expert Solution

This rule says that

Approximately 68% of the values lie within 1 standard deviation of the mean In statistical notation, this is represented as
Approximately 95% of the values lie within 2 standard deviations of the mean. The statistical notation for this is
99.7% of the values lie within 3 standard deviations of the mean. Statisticians use the following notation to represent this:

It is due to the probabilities associated with 1, 2, and 3 SD’s that the Empirical Rule is also known as the “68?95?99.7 rule”.

Now we have given that mean = 15 and standard deviation = 4 and we need to find the percentage of values in the distribution between 15 and 23 .percentage value between 15 and 23 = 34% + 13.5% = 47.5 %

milcah answered 1 year ago

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