Question

Which is relatively​ better: a score of 87 on a psychology test or a score of 52 on an economics​ test? Scores on the psychology test have a mean of 92 and a standard deviation of 5. Scores on the economics test have a mean of 62 and a standard deviation of 6.

Answer 1

To determine which score is relatively better, we need to use the concept of z-scores, which measure how many standard deviations a particular score is from the mean.

Step-by-step explanation:

To determine which score is relatively better, we need to use the concept of z-scores, which measure how many standard deviations a particular score is from the mean. The formula for calculating the z-score is:

z = (X - μ) / σ

where X is the score, μ is the mean, and σ is the standard deviation.

For the 87 on the psychology test:

z = (87 - 92) / 5 = -1

For the 52 on the economics test:

z = (52 - 62) / 6 = -1.67

Since a higher z-score indicates a score that is relatively better, we can conclude that the score of 87 on the psychology test is relatively better than the score of 52 on the economics test.

Answer 2

Answer: Psychology test score is relatively better than economics test score.

Step-by-step explanation:

For this question, we are using Z-score to compare the psychology test score and economics test score.

Z-scores are an approach to compare results from a test with a "normal" population.

Z =
`(X - u)/(S.D)`

where,

X - Test score

u - Mean

S.D - Standard deviation

Psychology Test:

Z =
`(87 - 92)/(5)`

=
`(-5)/(5)`

= -1

Economics Test:

Z =
`(52 - 62)/(6)`

=
`(-10)/(6)`

= -1.6

Hence, above calculation shows that z- score for pshychology test is greater than the z- score for economics test. so, psychology test score is better than economics test score.