Kindergarten children have heights that are normally distributed about a mean of 39 inches and a standard deviation of 2 inches. A random sample of size 25 is taken and the mean is calculated. Find the probability that the mean value (X-bar) will be between 38.5 and 40.0 inches.
Please explain.
Thanks
2007-04-30 15:11:00 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Do your own homework.
2007-04-30 15:14:53 · answer #1 · answered by Anonymous · 0⤊ 1⤋
Use the z-value to compute this. P(38.5 < x_bar < 40) =
P((38.5 - 39)/2/sqrt(25) < z < (40-39)/2/sqrt(25) ). Once you are done with the computation, use the standard normal distribution to find your probability.
2007-04-30 15:19:45 · answer #2 · answered by Cruffy 2 · 0⤊ 0⤋
We know the sample mean will be normally distributed with mean 39 inches and standard deviation 2 / √25 = 0.4 inches.
So P(38.5 <= X_ <= 40.0) = P(-0.5/0.4 <= Z <= 1.0/0.4)
= P(-1.25 <= Z <= 2.50)
= P(Z <= 2.50) - P(Z <= -1.25)
= 0.99379 - 0.10565 (5 d.p.)
= 0.88814 to 5 d.p.
2007-04-30 15:18:56 · answer #3 · answered by Scarlet Manuka 7 · 0⤊ 0⤋