In an autonomous community, three out of every five second-year high school students are enrolled in Mathematics II. Six students are randomly selected from all second-year high school students. It is requested: a) ( 0.75 points) Calculate the probability that exactly four of them are enrolled in Mathematics II. b) (0.75 points) Calculate the probability that at least one of them is enrolled in Mathematics II. c) (1 point) If an institute has 120 students enrolled in second-year high school, calculate, approximating the binomial distribution by a normal distribution, the probability that more than 60 of these students are enrolled in Mathematics II.
In an autonomous community, three out of every five second-year high school students are enrolled in Mathematics II. Six students are randomly selected from all second-year high school students.\\
It is requested:\\
a) ( 0.75 points) Calculate the probability that exactly four of them are enrolled in Mathematics II.\\
b) (0.75 points) Calculate the probability that at least one of them is enrolled in Mathematics II.\\
c) (1 point) If an institute has 120 students enrolled in second-year high school, calculate, approximating the binomial distribution by a normal distribution, the probability that more than 60 of these students are enrolled in Mathematics II.