SOLUTION: Suppose that the variable X is normally distributed with a mean of 200 and a standard deviation of 25. (i) What proportion of X-values lies between 180 and 205? (ii) Below wha

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose that the variable X is normally distributed with a mean of 200 and a standard deviation of 25. (i) What proportion of X-values lies between 180 and 205? (ii) Below wha      Log On


   

Question 301727: Suppose that the variable X is normally distributed
with a mean of 200 and a standard deviation of 25.
(i) What proportion of X-values lies between 180 and
205?
(ii) Below what value do 30 per cent of X-values lie?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the z score for 180 and 205.
z%28180%29=%28180-200%29%2F25=-0.8
z%28205%29=%28205-200%29%2F25=0.2
Now lookup the area under the curve for each z score (NORMDIST in EXCEL).
A%28180%29=0.2119
A%28205%29=0.5793
The difference in those is the area of interest to us.
A=0.3674
So almost 37% lies between 180 and 205.
.
..
The z score for 187 is 0.3015.
The z score for 186 is 0.2877.
The z score for 186.9 is 0.3001.
X=186.9