In a large class,the professor has each person toss a coin 200 times and calculate the proportion of his or her tosses that were tails.The students then report their results,and the professor records the proportions.One student claims to have tossed her coin 200 times and found 58% tails.What do you think of this claim? Explain your response.
A)This is a fairly unusual result.Her proportion is about 1.60 standard deviations above the mean.
B)This is a typical result.Her proportion is only 2.26 standard deviations above the mean.
C)This is a fairly unusual result.Her proportion is about 2.26 standard deviations above the mean.
D)This is an extremely unlikely result.Her proportion is about 200 standard deviations above the mean.
E)This is a typical result.Her proportion is only 1.60 standard deviations above the mean.

Question

Quizplus · Accepted Answer

Assuming a fair coin, the expected proportion of tails is 0.5. The standard deviation of the proportion of tails in 200 coin tosses is given by the formula sqrt(p(1-p)/n), where p is the proportion of tails and n is the sample size. Plugging in p=0.58 and n=200, we get a standard deviation of approximately 0.049. To find the number of standard deviations above the mean, we calculate (0.58 - 0.5)/0.049, which is approximately 1.64. This is close to but slightly higher than the 95% confidence level of 1.96, indicating that the result is fairly unusual but still within the realm of possibility. Therefore, the best choice is C).

In a Large Class,the Professor Has Each Person Toss a Coin