Final answer:
To find the probability of picking a raw score between the mean and 42, calculate the z-scores and find the area under the normal distribution curve.
Step-by-step explanation:
To find the probability of picking a raw score between the mean and 42, we need to first determine the z-scores for the mean and 42. The z-score represents how many standard deviations away a raw score is from the mean. With the information provided, we can calculate the z-scores as follows:
mean = (67.02 + 68.98) / 2 = 68
standard deviation = (68.98 - 67.02) / (2 * 1.96) = 0.9776
The z-score for the mean is 0, since it is the reference point. We can calculate the z-score for 42 as follows:
z-score = (42 - 68) / 0.9776 = -26.5252
To find the probability of picking a raw score between the mean and 42, we need to find the area under the normal distribution curve between the z-scores of 0 and -26.5252. Since the z-score of -26.5252 is extremely low, the probability of picking a raw score between the mean and 42 is almost 0.