Question

At a certain company, loan agents are paid based on the number of loans they close in a day. Based on company records, the number of loans XX that a randomly selected loan agent closes on a randomly selected day has the probability distribution below. At the company, the daily salary of a loan agent is $150 plus $50 per loan closed. Let Y represent the amount of money made by a randomly selected loan agent on a randomly selected day. Which of the following statements is NOT true? Responses The mean of X is less than the mean of Y. The mean of X is less than the mean of Y. The standard deviation of Y is approximately $71. The standard deviation of Y is approximately $71. The mean daily salary is greater than $350 per day. The mean daily salary is greater than $350 per day. The standard deviation of X is less than the standard deviation of Y. The standard deviation of X is less than the standard deviation of Y. The shape of the probability distribution of Y is unimodal and roughly symmetric.

Answer 1

The statement that is NOT true is: "The mean of X is less than the mean of Y."

In this scenario, X represents the number of loans closed, and Y represents the amount of money made by a loan agent. The mean of X is the average number of loans closed, while the mean of Y is the average amount of money made. Since each loan closed contributes $50 to the daily salary, the mean of Y is directly influenced by the mean of X. Therefore, the mean of Y will be greater than the mean of X, making the statement false.

The other statements about the standard deviation and shape of the probability distribution of Y are accurate in the context of the given information.