Question

In large-scale tree-felling operations, a machine cuts down trees, strips off the branches, and then cuts the trunks into logs of length X feet for transporting to a sawmill. It may be assumed that values of X are normally distributed with mean = 3 feet and a standard deviation of 0.50 feet.

The log is less than 2 feet.

A. 0.0228
B. 0.1587
C. 0.0228
D. 0.1587

Answer 1

To calculate the probability of a log being less than 2 feet long, we determine the Z-score and use a standard normal distribution table, which provides a probability of 0.0228 for a Z-score of -2.

Step-by-step explanation:

The question is concerned with finding the probability that a log is less than 2 feet long given a normal distribution of log lengths with a mean of 3 feet and a standard deviation of 0.5 feet. To find this probability, we can use the standard normal distribution (Z-score). The Z-score is calculated by subtracting the mean from the values of X and dividing by the standard deviation.

Here is how we calculate the Z-score for X = 2 feet:

Z = (X - mean) / standard deviation = (2 - 3) / 0.5 = -2.

After calculating the Z-score, we refer to the standard normal distribution table to find the associated probability. The probability of a Z-score less than -2 is 0.0228. Therefore, the correct answer is A. 0.0228.