Final answer:
To find the probability that the sample mean is between 53 and 54, we need to calculate the z-scores and find the area under the standard normal curve. The probability is approximately a) 0.0619.
Step-by-step explanation:
To find the probability that the sample mean is between 53 and 54, we need to calculate the z-scores for 53 and 54 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.
Using the given information, we have:
z1 = (53 - 50) / (15 / √35) ≈ 1.94
z2 = (54 - 50) / (15 / √35) ≈ 2.19
Next, we find the area under the standard normal curve between these two z-scores using a standard normal distribution table or a calculator. The probability is the difference between the two areas which is approximately 0.0619.
Therefore, the correct answer is a. 0.0619.