Final answer:
The symmetric and bell-shaped distribution of the weights of a sample of 1,275 cargo containers is a normal distribution. This distribution is characterized by its bell shape, where the mean, median, and mode all coincide.
Step-by-step explanation:
The type of distribution that is symmetric and bell-shaped, as described for the weights of a sample of 1,275 cargo containers, is the normal distribution. The uniform distribution is characterized by equal probability across its range, which is not bell-shaped. The exponential distribution describes the time between events in a Poisson process, and is not symmetric. The binomial distribution describes the number of successes in a sequence of independent experiments, and doesn't inherently have a bell shape (though it can approximate a normal distribution under certain conditions).
A normal distribution is specifically noted for its bell-shaped curve and symmetric properties about the mean; the mean, median, and mode of a perfectly normal distribution all coincide. Additionally, the central limit theorem supports the idea that, with a sufficiently large sample size, the distribution of the sample mean will approximate a normal distribution, even if the population from which the sample is drawn is not normally distributed.