Suppose Y is a random variable that follows a binomial distribution with n = 25 and π = 0.4. (a) Compute the exact binomial probability P(8 < Y < 14) and the normal approximation to this probability without using a continuity correction. Comment on the accuracy of this approximation. (b) Apply a continuity correction to the approximation in part (a). Comment on whether this seemed to improve the approximation.
frm binomial distribution: P(8<Y<14)= =0.6487
and std deviaiton =sqrt(np(1-p))=2.45
therefor from normal approximation:
error in approximation=|0.6487-0.7423|=0.0936
here the estimate is not accurate as the difference is singificantly high
from continuity correction
error in approximation=|0.6487-0.6527|=0.0040
this seems to be quite accurate as diffeence in approximation and actual is very low
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