For all these questions, please show all working and do not include codes, include screenshots for all tables for data and use excel for distribution tables and where needed.

1. The probability of flipping heads on a weighted coin is 65%. If the same coin is flipped 8 times and the number of heads, X, is counted,
   1. Is the distribution hypergeometric, uniform, normal, or binomial? How do you know?
   2. Make a probability distribution table and graph for the random variable X.
   3. Find the expected value and standard deviation of the experiment.
2. A modified deck of cards is created with two 2s, three 3s, four 4s, and five 5s. The random variable X is defined as the number of 3s drawn when 5 cards are picked without replacement, and the variable Y is defined as the number of 3s drawn when 5 cards are picked with replacement. 1. Make probability distribution tables for X and Y. 2. FInd the expected value of X and Y.
3. In Learning Activity 4.1, we said that a game is called fair when the expected value is 0. How much should the following game cost if it is supposed to be fair? Be sure to show all work, including a probability distribution table. Would this game be fun to play? A bag contains two red marbles, three black marbles, and six yellow marbles. A player draws two marbles from the bag without replacement. If they are the same colour, the player wins $10. If they are different colours, the player wins $20 per red marble, plus $10 per black marble, plus $5 per yellow marble.
4. MDM Farms grows normally distributed potatoes, and is testing a new crop. After 4 months, 20 plants produce potatoes with the following weights (in kg): 0.7, 1.4, 1.4, 1.3, 0.3, 1.4, 0.6, 1.3, 1.3, 1.1, 0.9, 1.5, 1.1, 1.5, 0.6, 1.4, 1.1, 0.5, 0.6, 0.8 1. Find the mean and standard deviation of the sample. 2. What percent of potatoes grown from this crop will be over 2 kg?
5. A police speed camera is set up to monitor vehicles on a stretch of road with a speed limit of 40 km/h. Long-term records for this location show that speeds follow a normal distribution with a mean of 48 km/h, and a standard deviation of 6 km/h. The speed camera will automatically ticket all drivers who exceed the limit by more than 10%. What percent of drivers will receive a ticket?
6. Marketing analysts for a juice manufacturer conducted a survey in a large town. They determined that the purchasing habits of consumers follow a normal distribution, with a standard deviation of 6 L of juice. A sample of 90 consumers showed a mean juice consumption of 25 L per household. Find a 90 and a 95% confidence interval for the true mean consumption.
7. A group of players is playing a game involving a special set of dice. A success on a single roll has a probability of 35.5%. a. An experiment is conducted by performing this roll 24 times and counting the number of successes. Is the normal approximation to the binomial theorem appropriate for this experiment? b. Regardless of your answer to part a, use the normal approximation to the binomial theorem to find the probability of getting more than 10 and fewer than 15 successes in 24 rolls.
8. Without further clarifying, a news report provided a binomial confidence interval to describe the probability of an event as between 0.591 and 0.749 based on an experiment with 25 trials. a. What was the margin of error in their interval? b. What was the success rate within the sample? c. What confidence level did they use?

REFERENCE: ILC ASSIGNMENT