(Question) A fair coin is tossed 150 times. Find the probability that between 40% and 50% (inclusive) of the tosses will result in heads.

(I know its possible to do this proportions but i prefer to do it with approximating the binomial distribution with the normal as i find it easier to figure out the continuity correction)

np = nq = 150*0.5 = 75. Greater than 5 therefore can use normal approximation

npq = 37.5 = variance

40% of 150 = 60 tree's

50% of 150 = 75 tree's

P(60 <= X <= 75) -> continuity correction -> P(59.5 < X < 75.5)

P( ((59.5-75)/(SQRT(37.5))) < Z < ((75.5 - 75)/(SQRT(37.5))) )

= 0.9943 + 0.5032 - 1

= 0.4975

Ans should be 0.527.

I dont believe its a rounding error so if someone could point out where i have gone wrong id appreciate it.

Thanks