just need the answers to make sure i did the right before i submit them
m&m’s chocolate candies come in six different colours. Suppose the colour distribution is as follows:
| Colour | Blue | Brown | Green | Orange | Red | Yellow |
| Probability | 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?
