Question 1180015
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I agree with the solution by @CPhill almost everywhere, except of its final part.


After the number of interest of heads is determined to be  between 28 and 30 inclusive,

the continuity correction should be applied.

Thus, actually, we look for the probability for H to be between 27.5 and 30.5.


So, in the solution by @CPhill the z-scores z1 and z2 should be modified consistently.


The final answer for the probability is then 0.2235 instead of 0.1498,
and the number of people between -8 and -4 meters is then about 0.2235*200 = 44.7,
or about 45.


This difference is significant and, therefore, should be accounted.