For a population of exam scores,a score of X = 83 corresponds to z = +0.50 and a score of X = 89 corresponds to z = +1.50.The population mean is μ = 80.

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Quizplus · Accepted Answer

This is true because we know that z-score = (X - μ)/σ, where X is the individual score, μ is the population mean, and σ is the standard deviation. We are given two data points: X = 83 corresponds to z = +0.50 and X = 89 corresponds to z = +1.50. Using these data points, we can set up two equations:

0.5 = (83 - 80)/σ
1.5 = (89 - 80)/σ

Solving for σ in each equation, we get:

σ = 6
σ = 3.33

Since the standard deviation cannot have two different values in the same population, we can assume that the second equation is incorrect. Therefore, the estimated standard deviation is σ = 6, which we can use to find the z-score for the population mean:

0 = (80 - 80)/6

This z-score is equal to 0, which tells us that the population mean is at the center of the distribution.

For a Population of Exam Scores,a Score of X =