Question

Decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

1. I haven't won in my last 25 pulls on the slot machine, so I'm due to win on the next pull

2. The larger a sample you take, the more the population looks like a normal distribution

3. The larger a sample you take, the closer the sample itself is to being normally distributed

Answer 1

1)False->The slot machine is a memory less process where every event is an independent event. Hence, the probability of winning doesnot depend on the previous turns. We can assume that the process gets reset after every pull

2)False-> The larger the population one takes, the mean of the sample gets closer to the thoeretical mean but doesnot say anything about the population looking like a normal distribution. However, when we keep sampling more and more time, the mean of the sample would tend to behave as a normal distribution.

3)False->The mean of the sample gets closer to the theoretical mean. Additionally the mean of the sample would start to behave close to the normal distribution.