SOLUTION: Consider a normal distribution with a mean of 50 and a standard deviation of 5. (a) Determine the probability that a random sample of 4 observations has a mean between49 and 52.

Question 1164666: Consider a normal distribution with a mean of 50 and a standard deviation of 5.
(a) Determine the probability that a random sample of 4 observations has a mean between49 and 52.
(b) Determine the probability that a random sample of 25 observations has a mean between 49 and 52.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the sd of the sample with 4 observations is 5/sqrt(4) or 2.5
so want z of (49-50)/2.5 which is -0.4
and z of 52 (52-50)/2.5 which is +0.8
this has probability of 0.4436
with 25, the sqrt is 5, so that distribution's sd is 4/5, or 0.8
this give a z of -1/0.8 or -1.25 and 2/0.8 or +2.5
that probability of z between those two values is 0.8881
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