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

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

Deleena Lowry · Accepted Answer

Final Answer : A, Explanation :  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% 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

Definitions

Learning Objectives

Learning Objectives

Related questions