Final answer:
To find the probability that the mean weight of the randomly selected cartons is greater than 10.21 ounces, calculate the z-score and use the z-table to find the probability. The probability is approximately 0.0085. None of the option is correct
Step-by-step explanation:
To find the probability that the mean weight of the randomly selected cartons is greater than 10.21 ounces, we need to calculate the z-score and then use the z-table to find the corresponding probability.
The z-score is calculated using the formula: z = (X - mu) / (sigma / sqrt(n)), where X is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.
In this case, X = 10.21 ounces, mu = 10 ounces, sigma = 0.5 ounces, and n = 25 (sample size).
Plugging these values into the formula, we get: z = (10.21 - 10) / (0.5 / √(25)) = 2.42.
Using the z-table, we find that the probability corresponding to a z-score of 2.42 is approximately 0.9915.
Therefore, the probability that the mean weight of the 25 cartons is greater than 10.21 ounces is approximately 1 - 0.9915 = 0.0085.
None of the option is correct