1. Simulate the result of tossing a fair coin 152 times, generating a list of 0s and 1s, with 152 entries, where 0 represents tails and 1 represents heads. Since the coin is supposed to be fair, you can use a uniform distribution with minimum 0 and maximum 1. Alternatively, you can use a Bernoulli distribution. What should the parameter p be? Use your simulation to estimate the probability of getting tails. Is is reasonable to expect at least 127 tails in 152 coin tosses? Why or why not? You may make a frequency distribution in order to analyze the results of the simulation.

2. Shaquille O’Neal is a professional basketball star who had a reputation for being a poor free throw shooter with a success rate of 0.528. Simulate the results of 200 free throws by creating a list with 200 entries, each either 0 (for a miss) or 1 (for a hit). Think about what distribution is appropriate here.
Repeat the simulation of free throws five times and record the number of times that the free throw was made. Is the percentage of successful free throws from the simulation reasonably close to 0.528 in each case? You may use an appropriate frequency table for this. Study the sequences of hits and misses, how long is the longest run of misses? How long is the longest run of hits? Compare this with your classmates.

3. The probability of randomly selecting an adult who recognizes the brand name of McDonald’s is 0.95. Conduct a simulation of size 10 and record the number of consumers who recognize the brand name of McDonald’s. Is the proportion of those who recognize McDonald’s reasonably close to the 0.95? Try another simulation this time with sample size 75. How do the results compare?