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

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

Elareera Asdecxz · Accepted Answer

Final Answer : A, Explanation :  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% 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

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