Question

Ten coins are flipped and the number of heads are counted. This process is repeated 100 times and the results are plotted in a histogram. Will the shape of the histogram resemble a normal curve?

Answer 1

Yes, the shape of the histogram will resemble a normal curve. For the given scenario, ten coins are flipped and the numbers of heads are counted. Consider flipping ten coins as a sample and proportion of heads in these ten coins as a parameter under interest. So, if we take 100 samples and find out the proportion of number of heads, then it will become a sampling distribution of the sample proportions and we know that sampling distribution of any sample statistic follows an approximate normal distribution although parent distribution is not normal. For this sampling distribution, we have µ_p̂ = 0.5.