Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 110.9-cm and a standard deviation of 0.6-cm. For shipment, 7 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is less than 110.9-cm.
P(M < 110.9-cm) = ______________

Enter your answer as a number accurate to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 110.9-cm

standard deviation = = 0.6-cm

n = 7

M = 110.9-cm

M = / n = 0.6 / 7 = 0.2268

P(M < 110.9-cm) = P((M - M) / M  < (110.9 - 110.9) / 0.2268)

= P(z < 0)

= 0.5000

P(M < 110.9-cm) = 0.5000