What is a 95 confidence interval for the probability of a p

What is a 95 % confidence interval for the probability of a piece of toast landing butter-side down?

Solution

Since n is large, we can use the normal approximation to the binomial. The interval will be

p ± z[p(1 - p)/n]

where p is the observed binomial proportion (6101/9821) = 0.621219835
z is the value for a standard normal distribution (95% confidence value is 1.96)
n is the sample size = 9821

0.621219835 ± 1.96[(0.621219835)(0.378780165)/9821]

= 0.6212 ± 1.962.39594E-05

= 0.6212 ± 0.0096

= (0.6116,0.6308)