Question

a coin, assumed to be fair, is flipped thirty six times. Five heads are observed. An approximate 95 percent confidence interval for this number of heads can be constructed, to two decimal places, as:

a(-1.09,11.09) b(0.00,10.88) c(0.07,9.95) d(-0.88,10.88) e(12.12,23.88)

Answer 1

The 95% confidence interval for number of heads = 5 Z/2 *

Here n = 36 which is the number of times the coin is flipped

p = Probability of a head upon toss of a coin which is 0.5 for a fair coin

p = 0.5

q = Probability of head not turning up on the toss of a coin which is also 0.5, since there are only two possibilities on toss of coin, Head and Tail. So the sum of both the probabilities is 1

q = 0.5

Here confidence level = 95% - 0.95

= 1 - confidence level

= 1 - 0.95

= 0.5

/2 = 0.025

The z-score than has an area of 0.975 to its left is 1.96 from the below attached table

So The 95% confidence interval for number of heads = 5 Z/2 *

= 5 1.96 *

= 5 1.96 *

= 5 1.96 * 3

= 5 5.88

= (-0.88, 10.88)

So The 95% confidence interval for number of heads is (-0.88, 10.88)