Answer:
No
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they can tell the difference between Coke and pepsi, or they cannot. The probability that a person has o telling the difference between Coke and pepsi is independent from each other. So we use the binomial probability distribution to solve this problem.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to the normal distribution if
and
In this problem, we have that:
First condition
Second condition
Multiplying by -1
p cannot be at the at the same time greather than 2/3 and lesser than 1/3. So we cannot assume that the sampling distribution of the proportion of people that correctly chose Pepsi is normal.