Final answer:
To find the minimum weight of a fish in the top 5%, we need to find the z-score corresponding to the top 5% and use the z-score formula. Similarly, to find the minimum weight of a fish to be mounted in the top 0.5%, we use the z-score formula. To determine the weights that delineate the middle 99%, we find the z-scores corresponding to the middle 0.5% and use the z-score formula to find the corresponding weights.
Step-by-step explanation:
In this question, we are given the weights of bass in Clear Lake that are normally distributed with a mean of 2.1 pounds and a standard deviation of 0.8 pounds. We are asked to find:
(a) The minimum weight of a fish that is in the top 5% as far as weight is concerned.
(b) The minimum weight of a fish to be mounted if it is in the top 0.5% of those in the lake.
(c) The weights that delineate the middle 99% of the bass in Clear Lake.
(a) To find the minimum weight of a fish that is in the top 5%, we need to find the z-score corresponding to the top 5% and then use the z-score formula to find the corresponding weight. The z-score formula is z = (x - mean) / standard deviation, where x is the weight we are looking for.
(b) To find the minimum weight of a fish to be mounted if it is in the top 0.5%, we need to find the z-score corresponding to the top 0.5% and then use the z-score formula to find the corresponding weight.
(c) To determine the weights that delineate the middle 99%, we need to find the z-scores corresponding to the middle 0.5% and then use the z-score formula to find the corresponding weights. The weights delineating the middle 99% will be the weights between these two z-scores.