A producer of flavoured milk is looking to alter the mix and flavour of their popular iced coffee. Traditionally 10% of all consumers purchase this brand.

The company decides to conduct a survey of iced coffee drinkers by running a taste test in a popular supermarket. If 20 customers are surveyed, and if there was no change in the proportion preferring this brand:

a.what is the probability that less than 2 would say they would purchase the new flavour? Use tables to calculate.

b.What is the probability that 3 or more would now say they would purchase this brand?

c.If they surveyed 200 people, what is the probability 30 or more would say they would purchase this brand? Use the =binom.dist function. What does this imply about whether or not the new flavour would be more popular if they did get 30 or more saying yes?

d.If they surveyed 2000 people what is the probability 300 or more would say they purchased this brand? What does this imply about the new flavour?

e.Comparing the results of b., c. and d. what can you say about the importance of sample size?

f.Calculate the Expected Value and Standard Deviation for the binomial experiment for each of b., c., and d.. What do you note about the relative risk of each of the three experiments