They used a formula in solutions but I dont understand the inequalities, formulas they used. Please mention what you use and the reason thanks

a$)200$ Bernoulli trials will be conducted. Between what values should the probability of success in one Bernoulli trial be$,$ so that the

application of the normal approximation to any question regarding the probability of numbers of successes produces a fairly accurate result?

b$)$ If $p=0\mathrm{.}045,$ find the exact value for $P(2x4),$ where $x$ is the binomial random variable representing the number of successes in $200$

trials.

c$)$ Find an approximate value for part $($b$)$ using the normal approximation. Is it ok to use the normal approximation in this case?

d$)$ Find an approximate value for part $($b$)$ using the Poisson approximation.The