with a mean of 19.6 inches, and standard deviation of 3.2 inches. If 47 items are chosen at random, what is the probability that their mean length is greater than 20.8 inches?

Answer 1

First off, let us get the parameters (assuming that the missing subject is some object with a length).

Sigma is 3.200 inches, Mu is 19.600 inches. Standard deviation of the mean or standard error is 3.2/√19.6. or .467 , and length test is 20.800 in (all to three decimal points accuracy)

To find the probability , since we know the population sigma , we use the Z or standard normal distribution.

Calculate Z as (20.8-19.6)/0.467 or 2.570

Looking this up (you can use a Z table, a calculator, or look up on line) the cumulative distribution for

P(Z >Z_test )= 1-0.995 or 0.51%

Remember to keep track of the direction of your comparison (greater than Zcrit or to the right) and the direction of the cumulative value given in the table you use. Some are right tailed and some are left tailed.