Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 170.5-cm and a standard deviation of 1.1-cm. For shipment, 12 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is between 171-cm and 171.5-cm. P(171-cm < M < 171.5-cm) = Enter your answer as a number accurate to 4 decimal places.

Answer 1

Solution :

Given that,

mean = = 170.5

standard deviation = = 1.1

n = 12

= 170.5

₌ / n = 1.1 12 = 0.3175

P (171 < M < 171.5 )

P ( 171 - 170.5 / 0.3175) < ( M -   / ) < ( 171.5 - 170.5 / 0.3175)

P ( 0.5 / 0.3175 < z < 1 / 0.3175 )

P (1.57 < z < 3.15 )

P ( z < 3.15 ) - P ( z < 1.57)

Using z table

= 0.9992 - 0.9418

= 0.0574

Probability = 0.0574