Question

Steel rods are manufactured with a mean length of 29 centimeter (cm) Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm.

(a) What proportion of rods has a length less than 28.9 am? (Round to four decimal places as needed.)

Answer 1

To find the proportion of rods with a length less than 28.9 cm, calculate the z-score using the mean and standard deviation, and use the standard normal distribution table.

Step-by-step explanation:

To find the proportion of rods with a length less than 28.9 cm, we need to calculate the z-score for this length and use the standard normal distribution table.

First, calculate the z-score using the formula: z = (x - μ) / σ, where x is the value we want to find the proportion for, μ is the mean length, and σ is the standard deviation.

Let's plug in the values: z = (28.9 - 29) / 0.06 = -1.6667.

Next, we can use a standard normal distribution table or a calculator to find the proportion corresponding to this z-score. The proportion is approximately 0.0478 (rounded to four decimal places).