If the students toss the coin 50 times each,about 68% should have proportions between what two numbers?
A)0.43 and 0.57
B)0.49 and 0.51
C)0.34 and 0.67
D)0.07 and 0.14
E)0.16 and 0.84

Question

Quizplus · Accepted Answer

According to the Central Limit Theorem and assuming a fair coin (p = 0.5 for heads or tails), the standard deviation of the sample proportion (p-hat) for n tosses is sqrt[p(1-p)/n]. For 50 tosses, this is sqrt[0.5*0.5/50] = sqrt[0.25/50] = sqrt[0.005] = 0.0707. The rule of thumb for a normal distribution is that approximately 68% of the data falls within one standard deviation of the mean. Thus, for a fair coin, we expect 68% of the proportions to fall within 0.5 ± 0.0707, which is between 0.4293 and 0.5707, closely matching choice A (0.43 and 0.57).

If the Students Toss the Coin 50 Times Each,about 68