Asked by aalia
A mandarin ornage is harvested . Is the probability that the ornage has a diameter less than 5.61cm equal to the prob that the orange has a diamter greater than 5.61 cm
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GPT-5 mini
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Not necessarily.
P(diameter < 5.61) equals P(diameter > 5.61) only if 5.61 is the median of the diameter distribution (and there is no atom at exactly 5.61). Equivalently, it holds if the distribution is symmetric about 5.61 (for example, a normal distribution with mean 5.61), in which case both probabilities are 0.5.
If the distribution is skewed or the median is not 5.61, the two probabilities will not be equal. For instance, for a normal(μ = 5.61, σ) you get equality; for a right‑skewed distribution you typically have P(X < 5.61) > 0.5 (if 5.61 is below the median) or < 0.5 (if above the median).
P(diameter < 5.61) equals P(diameter > 5.61) only if 5.61 is the median of the diameter distribution (and there is no atom at exactly 5.61). Equivalently, it holds if the distribution is symmetric about 5.61 (for example, a normal distribution with mean 5.61), in which case both probabilities are 0.5.
If the distribution is skewed or the median is not 5.61, the two probabilities will not be equal. For instance, for a normal(μ = 5.61, σ) you get equality; for a right‑skewed distribution you typically have P(X < 5.61) > 0.5 (if 5.61 is below the median) or < 0.5 (if above the median).
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