The median height of 1240 students in a school is 142 centimeres. The distributiim of the students heights is approximately symmetrical, and 248 of the students are more than 147 centimeters tall. What approximate percentile is represented by a height o f 137 centimeters?

Please Explain with detail.

If the distribution is symmetrical, then the mean = median = 142

248 students are taller than 247 cm

The percent of students taller than 247 = \frac{248}{1240} * 100 = 20%

This means that someone who is 247 cm is taller than 80% of the school

247 = 80th percentile

The 80th percentile is also 105 (247 - 142) cm away from the mean

Again as the graph is symmetrical, 20th percentile would be 105cm away from the mean as well

20th percentile = 142 - 105 = 37

The question is asking for percentile of 137 cm

Which lies in between 37 and 142, so the answer would be b/w 20 and 50

And will probably be a lot closer to 50 than 20 (because 137 is a lot closer to 142 than 37)

So, then answer will be something like 45th percentile

(Depending on the options)

What about if it is 147 instead of 247 cm tall?

mean = median = 142

147 = 80th percentile

The 80th percentile is 5 (147 - 142) cm away from the mean

Again as the graph is symmetrical, 20th percentile would be 5cm away from the mean as well

20th percentile = 142 - 5 = 137

Ans. 20th percentile