SOLUTION: A population of values has a normal distribution with μ=225.8 and σ=87.4. You intend to draw a random sample of size n=215. Find P82, which is the mean separating the

Algebra ->  Probability-and-statistics -> SOLUTION: A population of values has a normal distribution with μ=225.8 and σ=87.4. You intend to draw a random sample of size n=215. Find P82, which is the mean separating the       Log On


   

Question 1119446: A population of values has a normal distribution with μ=225.8 and σ=87.4. You intend to draw a random sample of size n=215.
Find P82, which is the mean separating the bottom 82% means from the top 18% means.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
population mean is 225.8
population standard deviation is 87.4
sample size is 215.

standard error = standard deviation divided by square root of sample size.

standard error = 87.4 / sqrt(215) = 5.960630527.

you look up in the normal distribution table, or use a normal distribution calculator, to find the z-score that is associated with 829% of the area under the normal distribution curve that is to the left of it.

i used the normal distribution calculator that is in the TI-84 Plus and came up with a z-score of .915365082.

to find the raw score associated with that, use the z-score formula of:

z = (x-m)/s

z is the z-score.
x is the raw score.
m is the mean
s is the standard error.

that formula becomes:

.915365082 = (x-225.8) / 5.960630527.

solve for x to get:

x = .915365082 * 5.960630527 + 225.8.

that results in x = 231.2561531.

that score will have 82% of the normal distribution curve to the left of it and 18% of the normal distribution curve to the right of it.

that means the probability of getting a raw score less than 231.2561531 is 82% and the probability of getting a raw score greater than 231.2561531 is 18%.

visually, this looks like this:

$$$

$$$

the first display shows you the proability of getting a raw score less than 231.2561.

the second display shows you the probability of getting a raw score greater than 231.2561.

round your answer as required.

any difference between what this online calculator shows you and the calculator i used has to do how many decimal places rounding has occurred.