You may need to use the appropriate appendix table or technology to answer this question.A binomial probability distribution has p $=0\mathrm{.}20$ and n $=100.($a$)$What are the mean and standard deviation?mean Correct: Your answer is correct.standard deviation Correct: Your answer is correct.$($b$)$Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.Yes, because np $5$ and n$(1$ p$)5.$No$,$ because np $<5$ and n$(1$ p$)<5.$ Yes, because n $30.$No$,$ because np $5$ and n$(1$ p$)5.$Yes, because np $<5$ and n$(1$ p$)<5.$Correct: Your answer is correct.$($c$)$What is the probability of exactly $25$ successes? Use the normal approximation of the binomial distribution to answer this question. $($Round your answer to four decimal places.$)$ Incorrect: Your answer is incorrect.$($d$)$What is the probability of $18$ to $22$ successes? Use the normal approximation of the binomial distribution to answer this question. $($Round your answer to four decimal places.$)($e$)$What is the probability of $13$ or fewer successes? Use the normal approximation of the binomial distribution to answer this question. $($Round your answer to four decimal places.$)$