Final answer:
To find the probability, calculate the z-score using the formula z = (x - μ) / (σ / √n) and use the z-table to find the probability corresponding to the z-score. The probability is approximately 0.002.
Step-by-step explanation:
To find the probability that the sample mean is greater than 54, we need to calculate the z-score and then use the z-table. The z-score is calculated using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values, we get: z = (54 - 50) / (10 / √49) = 4 / (10 / 7) = 2.8.
Referring to the z-table, we find that the probability of a z-score being greater than 2.8 is approximately 0.002, which corresponds to option a. 0.025 in the answer choices provided.