Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 232-cm and a standard deviation of 1.2-cm. For shipment, 26 steel rods are bundled together.

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 232-cm and a standard deviation of 1.2-cm. For shipment, 26 steel rods are bundled together.



Find the probability that the average length of a randomly selected bundle of steel rods is less than 231.9-cm.

P(M < 231.9-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

To find the probability that the average length of a randomly selected bundle of steel rods is less than 231.9-cm, calculate the z-score and find the corresponding probability from the z-table.

Step-by-step explanation:

To find the probability that the average length of a randomly selected bundle of steel rods is less than 231.9-cm, we need to calculate the z-score for this value and then find the corresponding probability from the z-table.

First, we calculate the z-score:

z = (231.9 - 232) / (1.2 / sqrt(26))

z = -1.41421

Next, we look up the probability corresponding to this z-score in the z-table. The probability is approximately 0.0786.

Therefore, P(M < 231.9-cm) ≈ 0.0786.