Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.6 feet and a standard deviation of 0.2 feet. A sample of 55 men's step lengths is taken.
Step 1 of 2: Find the probability that an individual man's step length is less than 2.3 feet. Round your answer to 4 decimal places, if necessary.
Answer 2'Points
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Step 1 ：We are given that the mean (\(\mu\)) of the step lengths of adult males is 2.6 feet and the standard deviation (\(\sigma\)) is 0.2 feet. We are asked to find the probability that an individual man's step length is less than 2.3 feet.

Step 2 ：This is a problem of normal distribution. We need to find the z-score for 2.3 feet and then find the corresponding probability.

Step 3 ：The z-score is calculated as \((X - \mu) / \sigma\), where X is the value we are interested in (2.3 feet in this case).

Step 4 ：Substituting the given values into the z-score formula, we get \(z = (2.3 - 2.6) / 0.2 = -1.5\).

Step 5 ：After finding the z-score, we can use a z-table to find the corresponding probability. The probability corresponding to a z-score of -1.5 is approximately 0.0668.

Step 6 ：Final Answer: The probability that an individual man's step length is less than 2.3 feet is approximately \(\boxed{0.0668}\).