The heights of all the students in a school are measured. It is found that the mean height is 156 cm and the standard deviation in 14 cm.What is the height of the 90th percentile?Give your answer to 1 decimal place.

Question

BlackTom AI · Accepted Answer

To find the 90th percentile, we treat the heights as roughly normally distributed with the given mean and standard deviation. We start by identifying the z-score that corresponds to the 90th percentile in a standard normal distribution. That z-value is about 1.2816. Next, we apply the transformation formula for a percentile in a normal distribution: percentile = mean + z * standard deviation. Here, mean = 156 cm and standard deviation = 14 cm. Multiplying: 1.2816 * 14 ≈ 17.9424. Adding to the mean gives 156 + 17.9424 ≈ 173.9424 cm. Rounding to one decimal place yields 173.9 cm.

If you’re double-checking, remember the key steps: identify the correct z for the percentile, scale by the standard deviation, and shift by the mean. Any small rounding during the multiplication will still land near 173.9 cm when rounded to one decimal place.

Potential misunderstandings to note: some learners might confuse percentiles with standard deviations or misremember the z-value for 90th percentile. Recalling that 90th percentile corresponds to a positive z around 1.28 helps keep the calculation on track. In this problem, converting that z into a height involves the linear transformation of the normal model: height = mean + z * sd.

The final value, expressed to one decimal place, is 173.9 cm.

The heights of all the students in a school are measured. It is found that the mean height is 156 cm and the standard deviation in 14 cm.What is the height of the 90th percentile?Give your answer to 1 decimal place.数值题

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