The weight of a randomly selected shipping container follows an unknown distribution with mean 12 tons and standard deviation 2 tons. Your cargo ship always carries a load of 100 randomly selected shipping containers.

a. What is the probability the load weighs more than 1,231 tons?
b. What is the 90th percentile of load weights?

I know that I need to use the z-score for part B, but I'm not sure how to find the probability of part A.

To find the probability that the load weighs more than 1,231 tons, we need to calculate the z-score and then find the corresponding cumulative probability.

Step 1: Calculate the z-score
The z-score formula is given by: z = (X - mean) / standard deviation
In this case, X = 1,231 tons, mean = 12 tons, and standard deviation = 2 tons.

z = (1,231 - 12) / 2
z = 1,219 / 2
z = 609.5

Step 2: Find the cumulative probability
Since we want to find the probability that the load weighs more than 1,231 tons, we need to find the area under the curve to the right of the z-score.

Using a standard normal distribution table or calculator, we find that the cumulative probability for a z-score of 609.5 is practically 1.

Therefore, the probability that the load weighs more than 1,231 tons is approximately 1.

Now let's move on to part B.

To find the 90th percentile of load weights, we need to find the value below which 90% of the load weights fall.

Step 1: Find the z-score corresponding to the 90th percentile
Since the standard normal distribution has a mean of 0 and a standard deviation of 1, we need to find the z-score that corresponds to the cumulative probability of 0.90.

Using a standard normal distribution table or calculator, we find that the z-score corresponding to a cumulative probability of 0.90 is approximately 1.28.

Step 2: Calculate the load weight at the 90th percentile
To calculate the load weight at the 90th percentile, we use the formula:
X = mean + (z * standard deviation)

X = 12 + (1.28 * 2)
X = 12 + 2.56
X = 14.56

Therefore, the 90th percentile of load weights is approximately 14.56 tons.