A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 109-cm and a standard deviation of 1.6-cm. For shipment, 27 steel rods are bundled together.

Question

Find the probability that the average length of a randomly selected bundle of steel rods is less than 108.7-cm. 

P(M < 108.7-cm) = 

Answer 1

mean (M) is N(109,1.6)

want to find P(M < 108.7)

convert to P(z < ???) using transformation to z-statistic which is N(0,1):

P(z < (M - population mean)/(standard deviation/square root(sample size)) =

P(z < (108.7-109)/(1.6/sqrt(27)) = P(z < -0.974) = 0.165.