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You can think of an individual coin flip as an independent Bernoulli trial. One trial will give you either heads/tails or success/failure, respectively. If you repeat this say 100,000 times, the average number of heads will be very close to 0.5, if the coin is fair.

Now if you increase the number of trials to 1,000 and keep the repetition at 1, you will get a sequence of 1,000 successes/failures and cannot say much about the probability of observing, on average, 500 heads unless you increase the number of repetitions for each of those independent trials. As the number of repetitions increases, you will get a better and better approximation to the normal distribution.

For me it is easier to think of the trials not as “tosses” or “sample sizes” but instead of separate coins and the repetitions as the number of flips of each of those coins. Then it also makes intuitively sense that by increasing the number of coins (or trials), while keeping the number of repetitions constant, the approximation of the data to the normal distribution gets worse.

You can think of an individual coin flip as an independent Bernoulli trial. One trial will give you either heads/tails or success/failure, respectively. If you repeat this say 100,000 times, the average number of heads will be very close to 0.5, if the coin is fair.

Now if you increase the number of trials to 1,000 and keep the repetition at 1, you will get a sequence of 1,000 successes/failures and cannot say much about the probability of observing, on average, 500 heads unless you increase the number of repetitions for each of those independent trials. As the number of repetitions increases, you will get a better and better approximation to the normal distribution.

For me it is easier to think of the trials not as “tosses” or “sample sizes” but instead of separate coins and the repetitions as the number of flips of each of those coins. Then it also makes intuitively sense that by increasing the number of coins (or trials), while keeping the total number of repetitions (or flips) constant, the approximation of the data to the normal distribution gets worse.

You can think of an individual coin flip as an independent Bernoulli trial. One trial will give you either heads/tails or success/failure, respectively. If you repeat this say 100,000 times, the average number of heads will be very close to 0.5, if the coin is fair.

Now if you increase the number of trials to 1,000 and keep the repetition at 1, you will get a sequence of 1,000 successes/failures and cannot say much about the probability of observing, on average, 500 heads unless you increase the number of repetitions for each of those independent trials. As the number of repetitions increases, you will get a better and better approximation to the normal distribution.

For me it is easier to think of the trials not as “tosses” or “sample sizes” but instead of separate coins (your x-axis) and the repetitions as the number of flips of each of those coins. Then it also makes intuitively sense that by increasing the number of coins (or trials), while keeping the number of repetitions constant, the approximation of the data to the normal distribution gets worse.

You can think of an individual coin flip as an independent Bernoulli trial. One trial will give you either heads/tails or success/failure, respectively. If you repeat this say 100,000 times, the average number of heads will be very close to 0.5, if the coin is fair.

Now if you increase the number of trials to 1,000 and keep the repetition at 1, you will get a sequence of 1,000 successes/failures and cannot say much about the probability of observing, on average, 500 heads unless you increase the number of repetitions for each of those independent trials. As the number of repetitions increases, you will get a better and better approximation to the normal distribution.

For me it is easier to think of the trials not as “tosses” or “sample sizes” but instead of separate coins and the repetitions as the number of flips of each of those coins. Then it also makes intuitively sense that by increasing the number of coins (or trials), while keeping the number of repetitions constant, the approximation of the data to the normal distribution gets worse.

You can think of an individual coin flip as an independent Bernoulli trial. One trial will give you either heads/tails or success/failure, respectively. If you repeat this say 100,000 times, the average number of heads will be close to 0.5, if the coin is fair.

Now if you increase the number of trials to 1,000 and keep the repetition at 1, you will get a sequence of 1,000 successes/failures and cannot say anything about the probability of observing, on average, 500 heads unless you increase the number of repetitions for each of those independent trials. As the number of repetitions increases, you will get a better and better approximation to the normal distribution.

For me it is easier to think of the trials not as “tosses” or “sample sizes” but instead of separate coins (your x-axis) and the repetitions as the number of flips of each of those coins. Then it also makes intuitively sense that by increasing the number of coins (or trials), while keeping the number of repetitions constant, the approximation of the data to the normal distribution gets worse.

You can think of an individual coin flip as an independent Bernoulli trial. One trial will give you either heads/tails or success/failure, respectively. If you repeat this say 100,000 times, the average number of heads will be very close to 0.5, if the coin is fair.

Now if you increase the number of trials to 1,000 and keep the repetition at 1, you will get a sequence of 1,000 successes/failures and cannot say much about the probability of observing, on average, 500 heads unless you increase the number of repetitions for each of those independent trials. As the number of repetitions increases, you will get a better and better approximation to the normal distribution.

For me it is easier to think of the trials not as “tosses” or “sample sizes” but instead of separate coins (your x-axis) and the repetitions as the number of flips of each of those coins. Then it also makes intuitively sense that by increasing the number of coins (or trials), while keeping the number of repetitions constant, the approximation of the data to the normal distribution gets worse.