Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 122.8-cm and a standard deviation of 0.6-cm. For shipment, 6 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is less than 122.7-cm.
P(M < 122.7-cm) =

Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Solution :

Given that ,

mean = = 122.8

standard deviation = = 0.6

n = 6

m = 122.8

m =  / n = 0.6 / 6=0.2449

P(M < 122.7) = P[(M - m ) / m < (122.7 -122.8) /0.2449 ]

= P(z < -0.408)

Using z table  

=0.3416

probability=0.3416