According to the National Institute of Statistics, during the last quarter of 2020, the percentage of women belonging to the set of Boards of Directors of companies that make up the Ibex-35 was 27.7 \%. Ten of these board members were gathered. a) ( 0.75 points) Find the probability that half were women. b) ( 0.75 points) Calculate the probability that there was at least one man. c) (1 point) Determine, approximating by a normal distribution, the probability that at a congress of two hundred board members of these companies there would be at least 35 \% female representation.
According to the National Institute of Statistics, during the last quarter of 2020, the percentage of women belonging to the set of Boards of Directors of companies that make up the Ibex-35 was 27.7 \%. Ten of these board members were gathered.\\
a) ( 0.75 points) Find the probability that half were women.\\
b) ( 0.75 points) Calculate the probability that there was at least one man.\\
c) (1 point) Determine, approximating by a normal distribution, the probability that at a congress of two hundred board members of these companies there would be at least 35 \% female representation.