4 The mean weight among a group of female high school senior

4. The mean weight among a group of female high school seniors is 120 lbs., with a standard deviation of 16.49 lbs. Assuming a normal distribution, find the percentiles for the following weight scores. a. 125 pounds b.90 pounds

Solution

Normal Distribution
Mean ( u ) =120
Standard Deviation ( sd )=16.49
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 125) = (125-120)/16.49
= 5/16.49= 0.3032
= P ( Z <0.3032) From Standard Normal Table
= 0.6191                  
b)
P(X < 90) = (90-120)/16.49
= -30/16.49= -1.8193
= P ( Z <-1.8193) From Standard Normal Table
= 0.0344