Mat 318

Lab 2

Do not hand in. Keep for your reference.

1. Simulating distributions in MINITAB

1. Rolling a die:

· Calc -> Random Data -> Integer. Generate 1 row, store in C1, minimum=1, maximum=6. This will produce a single number in column C1. It simulates rolling a standard die once.

· Generate 10 rows and look at the histogram.

· Try 100 rows. What is happening to the histograms?

· How many rows do you need to get really close to the ideal distribution? ________

2. Waiting for 6.
• Generate 10,000 rows using the geometric distribution with p=0.1666.
• Use your simulated data to estimate the probability of having to roll 12 or more times to get a 6. _______ Is this an unusual event?
• How many failures would it take to convince you that the die is not “fair”? _____

c. Counting cats.

· If 40% of people own a cat, how many cat owners will there be in a randomly selected group of 10 people? Generate 10,000 rows with n=10 and p=0.4.

• Each row represents the number of cat owners in a different possible sample. Since 10,000 is quite large, the histogram will closely resemble the probability histogram for the binomial distribution.
• Use your histogram to estimate the probability that

i. There are exactly 4 cat owners. ________

ii. There are at least 7 cat owners. ________

iii. There are 3 or fewer cat owners. ________

2. Shape of Binomial distribution

Experiment with different values of n and p. How does the shape depend on n and p?