Question

In: Statistics and Probability

A population is normally distributed with mean ? and standard deviation ?. Find the percentage of...

A population is normally distributed with mean ? and standard deviation ?. Find the percentage of values which are between ?−2? and ?+2?.

Expert Solution

Given Mean = ?

Standard Deviation = ?

The formual for Z-score = (X - Mean) / Standard Deviation

Z-score for X = ?−2? is

Z-score = (?−2? - ?) / ?

Z-score = -2

The area to the left of z-score of -2 is calculated by the below attached negative z-table.

The area to the left of z-score of -2 = 0.02275

Z-score for X = ?+2? is

Z-score = (?+2? - ?) / ?

Z-score = 2

The area to the left of z-score of 2 is calculated by the below attached positive z-table.

The area to the left of z-score of 2 = 0.97725

The area between ?−2? and ?+2? = 0.97725 - 0.02275

= 0.954975

So the percentage of values which are between ?−2? and ?+2? = 95.4975%

orchestra answered 1 year ago

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