High School

If the mean height is 180 cm and the standard deviation is 4 cm, what percentage of the population would lie between 176 cm and 180 cm?

A. 50%
B. 68%
C. 95%
D. 34%

Answer :

We can start by using the standard normal distribution to find the z-scores for the two heights:

z1 = (176 - 180) / 4 = -1

z2 = (180 - 180) / 4 = 0

Then, we can use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores. From a table, we find that the area to the left of -1 is 0.1587 and the area to the left of 0 is 0.5. Therefore, the area between -1 and 0 is:

0.5 - 0.1587 = 0.3413

To find the percentage of the population, we can convert this decimal to a percentage by multiplying by 100:

0.3413 x 100 = 34.13%

Therefore, approximately 34.13% of the population would lie between 176cm and 180cm in height.