To find the probability that LeBron records a score higher than 200, we'll use the properties of the normal distribution since we know the mean and standard deviation.
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Identify the parameters:
- Mean (\( \mu \)) = 180
- Standard Deviation (\( \sigma \)) = 28
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Calculate the z-score for 200: \[ z = \frac{X - \mu}{\sigma} = \frac{200 - 180}{28} = \frac{20}{28} \approx 0.7143 \]
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Use the z-score to find the probability: You can look up the z-score in a standard normal distribution table or use a calculator to find the probability of z being less than 0.7143.
Using a standard normal distribution table or calculator, the probability \( P(Z < 0.7143) \) approximately equals 0.7611 or 76.11%. Therefore, the probability of scoring higher than 200 is: \[ P(X > 200) = 1 - P(Z < 0.7143) \approx 1 - 0.7611 = 0.2389 \text{ or } 23.89% \]
From the provided options, the probability that LeBron records a score higher than 200 is closest to 23.8%.