Central Limit Theroy

#1
I have a problem i cant seem to figure out. X is from a population with u=53 and s=24. A sample size of 59 is taken from the population and an average is computed i need to fine P(xbar < 50.7). I know i need to use the zformual but im completely lost when it comes to that part, I know z= (x-u)/s , I cant seem to use that in the equation. I have the answers already and can't match them up. I just need a push in the right direction to help me through. Thanks alot.
 

JohnM

TS Contributor
#2
For finding the probability of an individual data point, z = (x-u)/s

For computing the probability of a particular sample mean, the z score formula is slightly different:

z = (x - u) / (s/sqrt(n))

where s/sqrt(n) = standard error of the means --> the standard deviation of sample means

z = (x - u) / (s/sqrt(n))

z = (50.7 - 53) / (24/sqrt(59))

= -2.3 / 3.125

= -0.736

Using the normal distribution table, find the probability that z < -0.736 since the question asks for the probability of getting a mean of < 50.7

you should get 23.1%