Final answer:
To find the probability that the mean height for the sample is greater than 64 inches, calculate the z-score using the sample mean, population mean, standard deviation, and sample size. Use the z-score and the standard normal distribution table to find the probability. The probability is approximately 0.5513, or 55.13%.
Step-by-step explanation:
To find the probability that the mean height for the sample is greater than 64 inches, we need to use the z-score formula and the standard deviation to standardize the sample mean and calculate the corresponding probability.
We start by finding the z-score 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.
Substituting the given values, we have z = (64 - 63.7) / (2.99 / √70) = 0.126.
Next, we find the probability using the z-score and the standard normal distribution table. Looking up the z-score of 0.126 in the table, we find that the probability is approximately 0.5513, or 55.13%.