If the students toss the coin 100 times each,about 95% should have proportions between what two numbers?
A)0.4 and 0.6
B)0.49 and 0.51
C)0.1 and 0.15
D)0.025 and 0.975
E)0.2375 and 0.7375

Question

Quizplus · Accepted Answer

The central limit theorem suggests that with a large number of trials, the distribution of the sample proportion of heads will be approximately normal, centered around the true proportion (0.5 for a fair coin), with a standard deviation equal to sqrt[(p(1-p))/n], where p is the true proportion and n is the number of trials. For 100 tosses, the standard deviation is sqrt[(0.5*0.5)/100] = 0.05. Using the 95% confidence interval, which typically corresponds to about 2 standard deviations from the mean in both directions, the range would be 0.5 ± 2*0.05 = 0.4 to 0.6.

If the Students Toss the Coin 100 Times Each,about 95