When choosing the right coffee beans for you, buying single-origin or blended coffee is another factor to consider. Buy single origin if you enjoy the body and flavour profile of specific coffee regions, and go for blend if you're happy with beans that have come from various geographic areas. Generally, the proportion of coffee beans that are single origin is 0.469.

Based on a randomly selected sample of 69 batches of coffee beans, 32 of them are single origin.

1. What is the distribution for the number of single origin coffee beans (X = 32)? Answer Binomial distribution Uniform distribution Normal distribution and write down the two parameters that determine the shape of this distribution, Answer (integer) and Answer (3dp)

Assuming we can make a normal approximation to Binomial distribution (Hint: check that conditions are satisfied). what is the probability that, in a random sample of 69 batches of coffee beans,

2. greater than 35 coffee beans are single origin? Answer (3dp)

3. no more than 24 coffee beans are single origin? Answer (3dp)

4. there are 25 and 42 coffee beans are single origin? Answer (3dp)