Statistics- what is the probability that exactly three of them are brown

QUESTION

just need the answers to make sure i did the right before i submit themm&m’s chocolate candies come in six different colours. Suppose the colour distribution is as follows:Colour Blue BrownGreenOrange Red YellowProbability 0.12 0.23 0.17 0.16 0.22 0.1(a) If you randomly select nine m&m’s, what is the probability that exactly three of them are brown? (b) If you randomly select 15 m&m’s, what is the probability that less than three of them are green? (c) If you randomly select 175 m&m’s, what is the approximate probability that at least 19% of them are orange?(d) If you randomly select 250 m&m’s, what is the approximate probability that between 21% and 27% of them are red? *Give all answers to four decimal places.A large lecture theater has 230 seats, 21 of which can accomodate left-handed students. Suppose it is known that 12% of people are left-handed. One class held in the theater has 209 students.(a) Let X be the number of left-handed students in the class. What are the mean and standard deviation of X?(b) Let be the proportion of left-handed students in the class. What are the mean and standard deviation of ?(c) What is the approximate probability that all left-handed students in the class get an appropriate desk?

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