A population of values has a normal distribution with μ = 35.3 μ = 35.3 and σ = 68.8 σ = 68.8 . You intend to draw a random sample of size n = 12 n = 12 .

Question

Find the probability that a single randomly selected value is greater than -10.4. 

P(X > -10.4) = 

Find the probability that a sample of size n=12n=12 is randomly selected with a mean greater than -10.4. 

P(M > -10.4) =

Answer 1

mean = 35.3

SD = 68.8

n = 12

x = value

M = mean

for single value z = (x - mean)/SD

P(x > -10.4) = P(z > (-10.4 - 35.3)/68.8) = P(z > -0.664) = 1 - P(z < -0.664) = 1 - 0.255 = 0.745

for mean value z = (M - mean)/(SD/square root(sample size))

P(M > -10.4) = P(z > (-10.4 -35.3)/(68.8/sqrt(12)) = P(z > -2.3) = 1 - P(z < 2.3) = 1 - 0.9893 = 0.0107