In: Statistics and Probability
The population mean and standard deviation are given below. Find the indicated probability and determine whether a sample mean in the given range below would be considered unusual. If convenient, use technology to find the probability. For a sample of n=3636, find the probability of a sample mean being less than 12, 752 or greater than 12,755 when μ =12,752 and σ =1.5
Solution :
Given that,
mean =
= 12752
standard deviation =
= 1.5
n = 3636
= 12752
=
/
n = 1.5 /
3636 = 0.0249
P(
<12752 ) = P((
-
) /
< (12752-12752 ) /0.0249 )
P(
< 12752) = P(Z < 0)
P(
< 12752) = 0.5 Using z table,
Probability = 0.5