Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 154.4 cm and a standard deviation of 2.2 cm.

Find , which is the length separating the shortest 45% rods from the longest 55%.

Answer 1

To find the length separating the shortest 45% rods from the longest 55%, calculate the z-scores corresponding to each percentage and use them to find the corresponding lengths.

Step-by-step explanation:

To find the length that separates the shortest 45% rods from the longest 55%, we need to find the z-score corresponding to each percentage.

The z-score for the shortest 45% is found by using the formula z = invNorm(0.45), which gives a z-score of approximately -0.1257.

Similarly, the z-score for the longest 55% is z = invNorm(0.55), which gives a z-score of approximately 0.1257.

Now, we can find the corresponding lengths by using the formula x = z * standard deviation + mean. Plugging in the values, we get:

x for the shortest 45% = -0.1257 * 2.2 + 154.4 = 154.1513 cm

x for the longest 55% = 0.1257 * 2.2 + 154.4 = 154.6487 cm

Therefore, the length separating the shortest 45% rods from the longest 55% is approximately 154.1513 cm - 154.6487 cm.