SolutionThe mean is 200 and the SD is + 10 or - 10 from the mean. As such , we do have a probability that ranging from 190 to 210. In total 20 numbers on our number line.

From this, we do have \(\frac{1}{20}\) of probability. This quantity is \(<\)\(\frac{1}{6}\)

The best answer is \(B\)

Alternative solution

Another approach to this problem is to draw a normal curve, or “bell-shaped curve,” that represents the probability distribution of the random variable Y, as shown.

The curve is symmetric about the mean 200. The values of 210, 220, and 230 are equally spaced to the right of 200 and represent 1, 2, and 3 standard deviations, respectively, above the mean. Similarly, the values of 190, 180, and 170 are 1, 2, and 3 standard deviations, respectively, below the mean. Quantity A, the probability of the event that the value of Y is greater than 220, is equal to the area of the shaded region as a fraction of the total area under the curve. i.e. the probability of the event that the value of Y is greater than 220 must be less than 5%, or \(\frac{1}{20}\) and this is certainly less than \(\frac{1}{6}\) The correct answer is \(B\).

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