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
[tex]np \geq 10[/tex]
and
[tex]n(1-p)\geq 10[/tex]
In this problem, we have that:
[tex]n = 15[/tex]
First condition
[tex]np \geq 10[/tex]
[tex]15p \geq 10[/tex]
[tex]p \geq \frac{10}{15}[/tex]
[tex]p \geq \frac{2}{3}[/tex]
Second condition
[tex]n(1-p) \geq 10[/tex]
[tex]15(1-p) \geq 10[/tex]
[tex]15 - 15p \geq 10[/tex]
[tex]-15p \geq -5[/tex]
Multiplying by -1
[tex]15p \leq 5[/tex]
[tex]p \leq \frac{1}{3}[/tex]
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.
