The mean height of a bull population is 150cm. The population shows a normal distribution with a standard deviation of 7cm. What will be the maximum height of bulls that are within 2 standard deviations of the mean?

Question

The mean height of a bull population is 150cm. The population shows a normal distribution with a standard deviation of 7cm. What will be the maximum height of bulls that are within 2 standard deviations of the mean?

BlackTom AI · Accepted Answer

Question restatement: The mean height of a bull population is 150 cm. The population shows a normal distribution with a standard deviation of 7 cm. What will be the maximum height of bulls that are within 2 standard deviations of the mean?

Answer options:
- 143 cm
- 171 cm
- 164 cm
- 157 cm

Option-by-option analysis:
Option 1: 143 cm. This value is 7 cm below the mean, i.e., mean − 1 SD (150 − 7 = 143). Being at −1 SD, it lies within 2 SDs, but the question asks for the maximum height within 2 SDs, not a point at another percentile. This option incorrectly seeks the lower bound at −1 SD, while the maximum within the 2-SD interval is higher.
Option 2: 171 cm. This is 21 cm above the mean, which corresponds to +3 SDs (since 3 × 7 = 21). Heights beyond +2 SD (which is 164 cm) are outside the specified range, so 171 cm is not within 2 standard deviations of the mean. This option overestimates the upper limit.
Option 3: 164 cm. This value equals the mean plus 2 SDs (150 + 2 × 7 = 164). It represents the upper bound of the interval from mean − 2 SD to mean + 2 SD. Therefore, 164 cm is the maximum height that still lies within 2 standard deviations of the mean.
Option 4: 157 cm. This is 1 SD above the mean (150 + 7 = 157). While it is within 2 SDs, it is not the maximum height within that range. The question asks for the maximum height within the 2-SD interval, so this is too low.

Summary: The 2-SD interval around the mean is from 150 − 2×7 = 136 cm to 150 + 2×7 = 164 cm. Among the options, 164 cm is the highest value still inside this interval, whereas the other options either lie outside the 2-SD range or are not the maximal value within it.

The mean height of a bull population is 150cm. The population shows a normal distribution with a standard deviation of 7cm. What will be the maximum height of bulls that are within 2 standard deviations of the mean?单项选择题

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