SOLUTION: A normal population has a mean of 12.2 and a standard deviation of 2.5. a. Compute the z value associated with 14.3. b. What proportion of the population is between 12.2 and 14.3

Algebra ->  Probability-and-statistics -> SOLUTION: A normal population has a mean of 12.2 and a standard deviation of 2.5. a. Compute the z value associated with 14.3. b. What proportion of the population is between 12.2 and 14.3      Log On


   

Question 239082: A normal population has a mean of 12.2 and a standard deviation of 2.5.
a. Compute the z value associated with 14.3.
b. What proportion of the population is between 12.2 and 14.3?
c. What proportion of the population is less than 10?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
z-score = (x-m)/s where:

x = score
m = mean
s = standard deviation.

in your problem:

m = 12.2
s = 2.5
x = 14.3

z-score (same as z-value) = (14.3-12.2)/2.5 = .84

proportion of the population between 12.2 and 14.3 is .299546

proportion of the population less than 10 is .189430

easiest way to find this out is to use the Z-Table Calculator

Go to the top graph.

Enter a mean of 12.2 and a standard deviation of 2.5

select "between" and enter 12.2 and 14.3.

Answer pops out at the bottom of the graph.

select "below" and enter 10.

Answer pops out at the bottom of the graph.

If you have to use the Z-Table without using the calculator it's more complicated.

If you need instructions for that, let me know.