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.

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, we need to calculate the z-score and find the corresponding probability using the standard normal distribution.

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 (P(M < 231.9-cm)), we need to calculate the z-score and then find the corresponding probability using the standard normal distribution.

Step 1: Calculate the z-score

z = (x - μ) / (σ / √n)

where x is the desired value (231.9), μ is the mean (232), σ is the standard deviation (1.2), and n is the sample size (26).

Plugging in the values, we get: z = (231.9 - 232) / (1.2 / √26) = -1.25

Step 2: Find the probability using the z-score

Using a z-table or a calculator, we can find that the probability corresponding to a z-score of -1.25 is approximately 0.1056.