You want to know the percentage of financial services companies that earned revenue between 36 36 million and 84 84 million dollars

Question

This problem has to do with Z-scores. 

 

You want to know the percentage of financial services companies that earned revenue between 36
36
million and 84
84
million dollars. If the mean revenue was 60
60
million dollars and the data has a standard deviation of 13
13
million, find the percentage. Assume that the distribution is normal. Round your answer to the nearest hundredth.

Answer 1

So you need to calculate your z score.

Your upper score is 24 from the mean...that's 24/13 standard deviations which is 1.846153 standard deviations above the mean.

Your lower score is 24 below the mean so that is also 1.846153 standard deviations from the mean.

 

So now look on your normal distribution table. I use the upper score and then subtract .5 or 50% since that is the percent less than the mean in a normal distribution.

 

So the table for 1.85 says .9678 or 96.78% of the people scored below 84. so 46.78% scored between the mean and 84. This is the same number for between 36 and the mean of 60.

 

So your answer is 46.78*2= 93.56%

 

Hope this helped