Answer :
Final answer:
The probability that a randomly selected board cut by the machine is approximately 1.0 (or 100%).
Explanation:
To find the probability that a randomly selected board cut by the machine, we need to convert the given values into z-scores and then find the corresponding probability using the standard normal distribution table or a calculator.
First, we calculate the z-score using the formula:
z = (x - mean) / standard deviation
where x is the length of the board.
Let's say we want to find the probability of a board with a length of 100 inches. Using the given mean of 97 inches and standard deviation of 0.4 inch, we can calculate the z-score:
z = (100 - 97) / 0.4 = 7.5
Next, we can use the standard normal distribution table or a calculator to find the probability corresponding to the z-score of 7.5. The table or calculator will give us the area under the standard normal curve to the left of the z-score.
Based on the calculated z-score, the probability can be found to be approximately 1.0 (or 100%).
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