Answer :
The probability that a randomly selected 10th grade boy exceeds 71 inches is approximately 5.05%.
The height of 10th grade boys is normally distributed with a mean (μ) of 66.9 inches and a standard deviation (σ) of 2.5 inches. To find the probability that a randomly selected 10th grade boy exceeds 71 inches, we can use the Z-score formula:
Z = (X - μ) / σ
Where Z is the Z-score, X is the height in question (71 inches), μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
Z = (71 - 66.9) / 2.5 = 4.1 / 2.5 ≈ 1.64
Now, we need to find the area to the right of the Z-score, which represents the probability that a randomly selected 10th grade boy exceeds 71 inches. Using a standard normal distribution table or a calculator with a built-in Z-score function, we find that the area to the right of Z = 1.64 is approximately 0.0505.
So, the probability that a randomly selected 10th grade boy exceeds 71 inches is approximately 5.05%.
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