Question 3 • Mathematics for College Liberal Arts Sem 1 (1207350) BCPS 2025-26
Which scenarios use the correct mean, population (μ), or sample (x̄) to represent the calculation? Check all that apply.A café owner wants to determine the average pay per week for all his employees. The mean should be calculated using population (μ).A scientist wants to determine how nitrogen levels affect the average height of some of the bean sprouts grown in his greenhouse. The mean should be calculated using population (μ).A psychology student surveys Dr. Kohl’s 10 a.m. English students about the number of hours they spend studying each week. The mean should be calculated using sample (x̄).A cattle rancher weighs each of his cattle every six months. He calculates the average weight. The mean should be calculated using population (μ).A running shoe distributor wants to know the average monthly inventory of a particular brand of shoe. He compiles the data from all the stores. The mean should be calculated using sample (x̄).
Answer
A
A café owner wants to determine the average pay per week for all his employees. The mean should be calculated using population (μ).
B
A scientist wants to determine how nitrogen levels affect the average height of some of the bean sprouts grown in his greenhouse. The mean should be calculated using population (μ).
C
A psychology student surveys Dr. Kohl’s 10 a.m. English students about the number of hours they spend studying each week. The mean should be calculated using sample (x̄).
D
A cattle rancher weighs each of his cattle every six months. He calculates the average weight. The mean should be calculated using population (μ).
E
A running shoe distributor wants to know the average monthly inventory of a particular brand of shoe. He compiles the data from all the stores. The mean should be calculated using sample (x̄).
Explanation
Use the population mean μ when the data include the entire group of interest, and the sample mean x̄ when they include only part of that group. The café owner includes all employees, and the rancher weighs every one of his cattle, so A and D correctly use μ. The psychology student surveys a group of students as a sample, so C correctly uses x̄. B describes only some sprouts, so it should use x̄; E includes data from all stores, so it should use μ.
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