Final answer:
To find the probability that the sample mean will be less than 250 lb., we need to calculate the z-score and find the corresponding probability using the z-table or a statistical calculator.
Step-by-step explanation:
To solve this problem, we need to calculate the z-score for the sample mean. The formula for calculating the z-score is:
z = (x - μ) / (σ / sqrt(n))
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, the sample mean is 250 lb., the population mean is 245.86 lb., the population standard deviation is 20 lb., and the sample size is 50.
Substituting these values into the formula, we get:
z = (250 - 245.86) / (20 / sqrt(50))
z = 4.14 / (20 / 7.07)
z = 0.7316
Next, we need to find the probability corresponding to this z-score using the z-table or a statistical calculator.