A population of values has a normal distribution with μ=128.6 and σ=43.9. You intend to draw a random sample of size n=119.
Find the probability that a single randomly selected value is between 116.5 and 123.4.
P(116.5 < X < 123.4) =
To use standard normal probability table need to convert end-points of above range to z-scores:
z-score = (value - population mean)/standard deviation
For 116.5 it is (116.5-128.6)/43.9 = -0.276
For 123.4 it is (123.4-128.6)/43.9 = -0.118
So range becomes:
P(-0.276 < Z < -0.118) = P(Z < -0.118) - P(Z < -0.276), which can be found from standard normal probability tables.
Find the probability that a sample of size n=119 is randomly selected with a mean between 116.5 and 123.4.P(116.5 < M < 123.4) =
To use standard normal probability table need to convert end-points of above range to z-scores:
z-score = (sample mean - population mean)/(standard deviation/square root of sample size)
For 116.5 it is (116.5-128.6)/(43.9/sqrt(119)) = -3.007
For 123.4 it is (123.4-128.6)/(43.9/sqrt(119)) = -1.292
So range becomes (-3.007 < Z < -1.292) = P(Z < -1.292) - P(Z < -3.007)
