A normal distribution has a mean of 142 and a standard deviation of 16. What is the probability that a randomly selected value lies between 142 and 174?

Question

A normal distribution has a mean of 142 and a standard deviation of 16.

What is the probability that a randomly selected value lies between 142 and 174?

Answer 1

Start off by counting how many SDs each end point is from the mean.

 

142-142/16 = 0 SD

 

174-142/16 = 2 SD

 

Recall by the 68-95-99.7 rule that 95% of the distribution is within 2 SDs of BOTH sides of the mean.  However, we are only going 2 SDs to the right of the mean (on the left, we are placed exactly at the mean).  So we are only encompassing half of 95% of the distribution, which is 47.5%.

 

 

You can use this picture for a visual representation of the answer: http://moodle2.rockyview.ab.ca/pluginfile.php/63427/mod_book/chapter/24271/m20_2_m4/images/m4/m20_2_m4_050.jpg