Final answer:
To find the probability that the sample mean would differ from the population mean by greater than 1.5 kilograms, calculate the z-score and use the standard normal distribution table. The probability is 0.0.
Step-by-step explanation:
To find the probability that the sample mean would differ from the population mean by greater than 1.5 kilograms, we need to calculate the z-score for the given difference and then find the corresponding probability using the standard normal distribution table.
The formula to calculate the z-score is:
z = (x - μ) / (σ / √(n))
where:
x = sample mean difference (1.5 kg)
μ = population mean (68 kg)
σ = population standard deviation (10 kg)
n = sample size (128)
Substituting the given values, we get:
z = (1.5 - 68) / (10 / √(128))
Simplifying the equation, we get:
z = -6.5
Using the standard normal distribution table, we find that the probability of obtaining a z-score of -6.5 or greater is approximately 0.0. Therefore, the probability that the sample mean would differ from the population mean by greater than 1.5 kilograms is 0.0 (rounded to four decimal places).