Math homework help

Question

The distribution of the weights of 100 students has a mean of 168lbs with a standard deviation of 16lbs. Predict the number of students who have weights between 135 and 175 pounds.

Answer 1

Hello Mike,

First, find your z-scores for the two values. 

Therefore,

z = 135 - 100
     _________
          16 

z = -2.06   <------------------------z score for 135 lb value 


Therefore: 

z = 175 - 168
      ________
            16    

z = .43        <-----------------------z score for 175 lb. value 


Next: Find the probabilities for each of these z-scores. 

You may use this particular link which provides both negative and positive z score probabilities 

http://www.z-table.com/


For z score of -2.06 you will see the probability is .0197 
For z score of    .43 you will see the probability is .6664


Subtract your probabilities: 

.6664
.0197
_____

.6467

Since you need to know the number of students you must convert this to a percentage by multiplying by 100


.6467 
x 100
_____
64.70%  

N = 100 


Therefore, 65 percent (I round up) of the 100 students will fall between 135 and 175. 

100 x 65% = 65 

65 students. 

Hope this helps and you have a great day. Please feel free to answer back to let me know you understood all.