Final answer:
To find the proportion of cockroaches with weights greater than 83 grams, we can use the properties of the normal distribution. The correct option is a. 20%.
Step-by-step explanation:
To find the proportion of cockroaches that will have weights greater than 83 grams, we need to know the distribution of weights. Let's assume that the weights of cockroaches follow a normal distribution. Using the properties of the normal distribution, we can calculate the proportion by finding the area under the normal curve to the right of 83 grams.
To calculate this proportion, we can use a Z-score table or a statistical calculator. For example, if we assume a standard normal distribution, the Z-score corresponding to a weight of 83 grams is approximately 0.80. Looking up this Z-score in the Z-score table or using a statistical calculator, we can find that the proportion of weights greater than 83 grams is approximately 0.2119, which is equivalent to 21.19%. Therefore, the correct option is a. 20%.