Mr. Antwine bought a "trick" quarter from a store the other day.The packaging said that this quarter would flip heads 80% of the time. After leaving the store, Mr. Antwine thought that maybe the quarter is not a "trick" and he just bought a regular quarter for 3 Mr. Antwine then decided to test his quarter. He flipped the quarter 40 times and recorded the number of heads that he got. He got 65% heads out of 40 tosses. What should he conclude? The coin is a trick coin because .65 is less than 5% The coin is a trick coin because 2.88% is less than 5% The coin is not a trick coin because it is not that unusual to flip 65% heads. There is not enough information to figure this out. The coin is not a trick coin because 1.97 is greater than 5%

To determine whether the quarter Mr. Antwine bought is a "trick" coin or not, we need to compare the proportion of heads he got from flipping the quarter 40 times with the proportion of heads that the packaging claimed the "trick" quarter would flip.<br /><br />The packaging claimed that the "trick" quarter would flip heads 80% of the time. This means that if the quarter is indeed a "trick" coin, we would expect it to flip heads 80% of the time.<br /><br />Mr. Antwine flipped the quarter 40 times and recorded the number of heads he got. He got 65% heads out of 40 tosses. This means that he got 26 heads out of 40 flips.<br /><br />To determine whether this is unusual, we can calculate the standard deviation of the proportion of heads for a "trick" coin that flips heads 80% of the time. The standard deviation can be calculated using the formula:<br /><br />Standard deviation = sqrt(p * (1-p) / n)<br /><br />where p is the proportion of heads (0.8) and n is the number of flips (40).<br /><br />Plugging in the values, we get:<br /><br />Standard deviation = sqrt(0.8 * (1-0.8) / 40) = 0.05<br /><br />Now, we can calculate the z-score for the proportion of heads Mr. Antwine got (0.65) using the formula:<br /><br />z-score = (sample proportion - population proportion) / standard deviation<br /><br />Plugging in the values, we get:<br /><br />z-score = (0.65 - 0.8) / 0.05 = -3.4<br /><br />A z-score of -3.4 indicates that the proportion of heads Mr. Antwine got is 3.4 standard deviations below the expected proportion for a "trick" coin. This is a very unusual result, as it falls more than 3 standard deviations below the mean.<br /><br />Therefore, we can conclude that the coin is not a trick coin because it is not that unusual to flip 65% heads.