Question 1194451
b and c first. Use a normal approximation for a skewed distribution binomial with small n and p=0.9, and it will have more error.
If a binomial is completely symmetrical, it may be approximated by a normal distribution quite well with small np or n(1-p).

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A baseball player is batting 0.400. What is the probability he will get no more than 10 hits in the next 50 at bats? The exact is 0.00076 or 0.0008 probability

look at 50C9*0.40^9*0.60^41=0.000527
for 8 hits 0.000169, and this for the others will converge to the exact.
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np=20 hits mean
np(1-p)=20*0.6=12 hits variance; SD is sqrt(V)=3.464 hits

probability of z < 9.5 is z(9.5-20)/3.464=-3.03
The probability  of z < -3.03 is 0.0012, a decent approximation.