Question

Suppose you are asked to toss a coin 16 times and calculate the proportion of the tosses that were heads.

a.    What shape would you expect this histogram to be and why?
b.    Where you do expect the histogram to be centered?
c.    How much variability would you expect among these proportions?
d.    Explain why a Normal model should not be used here.

Answer 1

Solution

a)

We need to identify the shape of the distribution.

Here on thing should be noted that, probability of heads and tails is equal. In that case shape of the distribution must be symmetric. Hence, it can be say that shape of the distribution is symmetric.

b)Here there are equal chance of head and tail. Total probability is 1. So there are 0.5 is the probability of head. Hence if we draw a histogram, it is expected to be centered at p=0.5

c)Variability can be calculated as,

d)Here to check the distribution is normal or not, we need to check condition of normal approximation to binomial.