Assume there are two lakes containing trout and the weights of the trout in each lake are normally distributed. The distribution of trout weight in Lake A has a mean of 18 ounces with a standard deviation of 2 ounces. The distribution of trout weight in Lake B has a mean of 19 ounces and a standard deviation of 3 ounces. Which of the following statements is NOT true?
What statements?
To determine which of the given statements is not true, we need to examine each statement and check if it aligns with the information provided about the two lakes.
Statement 1: "The average weight of trout in Lake A is higher than the average weight of trout in Lake B."
To compare the average weights, we need to compare the means of the two lakes. Since the mean of trout weight in Lake B is 19 ounces and the mean of trout weight in Lake A is 18 ounces, this statement is false.
Statement 2: "The spread of trout weights in Lake B is greater than the spread of trout weights in Lake A."
To compare the spread, we need to compare the standard deviations of the two lakes. Since the standard deviation of trout weight in Lake B is 3 ounces and the standard deviation of trout weight in Lake A is 2 ounces, this statement is true.
Statement 3: "There is a higher probability of catching a heavy trout in Lake A compared to Lake B."
To determine the probability, we need to compare the areas under the curves of the two normal distributions. Since we do not have specific values or probabilities, we cannot determine whether this statement is true or false based on the given information.
Given that Statement 1 is false and Statement 2 is true, the statement that is NOT true is Statement 1: "The average weight of trout in Lake A is higher than the average weight of trout in Lake B."