In: Statistics and Probability
A population has mean μ = 16 and standard deviation σ = 1.5. A random sample of size n = 49 is selected. What is the probability that the sample mean is greater than 16.8?
I got 3.73 for z-value.
Please help
Population has a mean =16 and standard deviation = 1.5.
Random sample of size n =49
Sample mean follows normal with mean =16 and standard deviation :
probability that the sample mean is greater than 16.8
i.e P( > 16.8) = 1-P(16.8)
Z -score for 16.8 = (16.8 - 16)/0.2143 = 3.73
From standard normal tables;
P(Z3.73) = 1.000
Generally Standard normal tables are available from -3.5 to 3.5
Any Z Value beyond 3.5 can be taken as 1.0
Also using Excel function : NORM.S.DIST(3.73,1) the value of P(Z3.73) = 0.9999
P(16.8) = P(Z3.73) =1.0
P( > 16.8) = 1-P(16.8) = 1-1.0 = 0