Final answer:
To find the probability that the sample mean is between 68.5kg and 71.3kg, calculate the z-scores of these values and find the area under the normal curve between them. The probability is approximately 0.549, closest to answer choice A. 0.58.
Step-by-step explanation:
To find the probability that the sample mean is between 68.5kg and 71.3kg, we need to calculate the z-scores corresponding to these values.
The z-score formula is: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.
Using the given information: μ = 70kg, σ = √25kg = 5kg, and n = 72.
Calculating the z-scores:
z1 = (68.5 - 70) / (5 / √72) = -1.63
z2 = (71.3 - 70) / (5 / √72) = 1.80
The probability that the sample mean is between 68.5kg and 71.3kg can be found by calculating the area under the normal curve between these two z-scores.
Using a z-table or a calculator, we find that the area between -1.63 and 1.80 is approximately 0.549.
Therefore, the probability that the sample mean is between 68.5kg and 71.3kg is 0.549, which is closest to answer choice A. 0.58.