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Last week Sarah had exams in math and in Spanish. On the math exam, the mean was µ = 40 with σ = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with σ = 8, and Sarah had a score of X = 68. For which class should Sara expect the better grade?​

Respuesta :

Answer:

The grades should be the same because the two z scores are same

Step-by-step explanation:

We are given the following information in the question:

Math

Mean, μ = 40

Standard Deviation, σ = 5

Math's score = 45

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

Putting values, we get

[tex]z_{score} = \displaystyle\frac{45-40}{5} = 1[/tex]

Spanish

Mean, μ = 60

Standard Deviation, σ = 8

Spanish's score = 68

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

Putting values, we get

[tex]z_{score} = \displaystyle\frac{68-60}{8} = 1[/tex]

Thus, both have the same z-score, we can say that, the grades should be the same because the two scores are in the same location and have the same z-score.