Final answer:
To find the z-score for a given two-tail probability, we need to use the Z-table and calculate the area between the two tail probabilities. None of the answer choices provided is correct.
Step-by-step explanation:
To find the z-score for which the two-tail probability that falls more than z standard deviations from the mean in either direction equals 0.38, we can use the Z-table. First, we need to find the area to the left of each z-score given in the answer choices:
- For z = 0.43, the area to the left is 0.6664.
- For z = 1.94, the area to the left is 0.9736.
- For z = 0.67, the area to the left is 0.7486.
- For z = 1.75, the area to the left is 0.9599.
Next, we subtract the smaller area from the larger area to get the area between the two tail probabilities: 0.9736 - 0.6664 = 0.3072.
This area represents the two-tail probability, so we divide it by 2 to get the probability in each tail: 0.3072 / 2 = 0.1536.
Finally, we find the z-score that corresponds to this probability by looking it up in the Z-table. The closest value is 1.03.
Therefore, the correct z-score is 1.03, so none of the answer choices (a, b, c, or d) is correct.