IMPORTANT NOTE: THE SOLUTIONS MUST BE PROVIDED IN "R" CODE

QUESTION: The normal distribution may be used to approximate the binomial distribution if np > 5 and np(1-p) > 5. Find the following binomial probabilities using *dbinom()* and *pbinom()* with a probability, p = 0.5, and n = 100. Then, estimate the same probabilities using the normal approximation **with continuity correction** and *pnorm()*.

(i) The probability of exactly 50 successes.

(ii) The probability of fewer than 40 successes.

(iii) The probability of 60 or more successes.