Assume that a normal distribution of data has a mean of 17 a

Assume that a normal distribution of data has a mean of 17 and a standard deviation of 3. Use the 68-95-99. 7 rule to find the percentage of values that lie about 20. What percentage of values lie about 20?

___% (Type an integer or a decimal.)

Solution

For values to lie above 20, they have to be [ (20-17)/3 ] stadnard deviations above mean.
20-17=3; 3/3=1; Thus we have to find the percentage of values that lie above mean+1 stanndard deviation;

The 68-95-99.7 rule states that there are 68% of total values in a normal distribution curve that lie between mean +/- 1*standard deviation; So 32% do not lie in this range. Since normal curve is symmetric, it means that half of 32% will lie above mean+ 1*standard deviation and the other half will lie below mean-1*standard deviation;

So 16% lie above mean+ 1*standard deviation which is 17+3=20;
Thus, using the 68-95-99.7 rule it can be said that 16% of the total values will lie above 20

Answer=16%