Question 1119280: . Find the probabilities that a random variable will take on a value between 10 and 20 given that it has a normal distribution with:
(a) Mean = 10 and s = 5
(b) Mean = 20 and s = 10
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The z-score for any value=(x-mean)/sd
For value between 10 and 20, the z score is between 0 and +2
That is probability between 0.5000 and 0.9772, so the actual probability is the difference between the two or 0.4772
For the second, this is the probability of z being between -1 or (10-20)/10 and 0. The second has probability of 0.5000 and the first 0.1587, and the difference is 0.3413, which represents the probability being between the values of 10 and 20.
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