Final answer:
To find the probability of a sample proportion of 111 / 298 or more, given that the true proportion is 0.34, we can use the normal distribution and standard error formula.
Step-by-step explanation:
The problem asks to find the probability of a sample proportion of 111 / 298 or more, given that the true proportion is 0.34. To solve this, we need to use the normal distribution and the standard error formula: SE = sqrt((p * q) / n), where p is the true proportion, q is 1 - p, and n is the sample size. Based on the given information, we have p = 0.34, q = 0.66, and n = 298. Plugging these values into the formula, we have SE = sqrt((0.34 * 0.66) / 298) = 0.029. Next, we calculate the z-score using the formula: z = (x - p) / SE, where x is the sample proportion we want to find the probability for. In this case, x = 111 / 298. Plugging in the values, we have z = (111 / 298 - 0.34) / 0.029 = -4.48. Finally, we use the z-table or a calculator to find the probability associated with a z-score of -4.48, which is approximately 0.00001 (or 0.001%). Therefore, the probability of a sample proportion of 111 / 298 or more, given that the true proportion is 0.34, is approximately 0.00001.