I have questions about R language. About 2b and 2b, I am confused with "fewer than." About 2a and 3a, I am not sure the reason why we can use np. About 3c, I think the output is not correct, but I have no idea where I should fix the code.

Thanks,

2. Dr. Keaton is still terrible at throwing darts. Each time he throws a dart, there is a probability of 0.01 that he hits the bullseye. He throws 100 darts. a. Is it appropriate to use the Normal approximation to the Binomial here? Why or why not? b. Regardless of your answer to part a, use the Normal approximation to find the probability that Dr. Keaton hits the bullseye fewer than 2 times (that is, 1 or fewer times). c. Use the Binomial distribution to find the exact probability that Dr. Keaton hits the bullseye fewer than 2 times. 3. Dr. Craig is still better at throwing darts. Each time he throws a dart, there is a probability of 0.30 that he hits the bullseye. He throws 100 darts. [Note: You should be able to reuse most of your code from question 2.] a. Is it appropriate to use the Normal approximation to the Binomial here? Why or why not? b. Regardless of your answer to part a, use the Normal approximation to find the probability that Dr. Craig hits the bullseye fewer than 36 times (that is, 35 or fewer times). c. Use the Binomial distribution to find the exact probability that Dr. Craig hits the bullseye fewer than 36 times