Solution of problem N1125 Laplace probability theory

1125. The probability of hitting a target with one shot is 0.4. 600 shots were fired. To find:
a) boundaries in which the probability of 0.9949 will be the number of hits on the target;
b) the number of shots to be fired on the target, so that with a probability of 0.9949 one could expect that the deviation of the hit frequency from one shot from its probability would be less than 0.05 (in absolute value).