The scores in a national test have a mean of 200 and standard deviation of 10.

The scores are continuous and distributed symmetrically about the mean. Of

the following numbers which is the largest possible value for the probability

that the score of a randomly chosen candidate is at least 215?

(A) 0.214 (B) 0.216 (C) 0.218 (D) 0.220 (E) 0.224

Let X be the score. Since the distribution of the score is symmetric about

the mean, using Chebyshevâ€™s inequality,

Pr(X>215) = (1/2)Pr[|X − 200|>15]<(1/2)(10/15)^2 = 2/9.

The largest of the given numbers that satisfies this is 0.22.

My question is why we need to multiply 1/2 ?? Is something related to "The scores are continuous and distributed symmetrically about the mean"??

Please help me!! Thank you very much!!

10 more days.........

The scores are continuous and distributed symmetrically about the mean. Of

the following numbers which is the largest possible value for the probability

that the score of a randomly chosen candidate is at least 215?

(A) 0.214 (B) 0.216 (C) 0.218 (D) 0.220 (E) 0.224

Let X be the score. Since the distribution of the score is symmetric about

the mean, using Chebyshevâ€™s inequality,

Pr(X>215) = (1/2)Pr[|X − 200|>15]<(1/2)(10/15)^2 = 2/9.

The largest of the given numbers that satisfies this is 0.22.

My question is why we need to multiply 1/2 ?? Is something related to "The scores are continuous and distributed symmetrically about the mean"??

Please help me!! Thank you very much!!

10 more days.........

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