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# The college physical education department offered an advanced first aid course last semester. The scores on the comprehensive final exam were normally

Normal distributions
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asked 2021-05-18
The college physical education department offered an advanced first aid course last semester. The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below: Robert, 1.10 Juan, 1.70 Susan, -2.00 Joel, 0.00 Jan, -0.80 Linda, 1.60 If the mean score was &mu;=150&mu;=150 with standard deviation &sigma;=20,&sigma;=20, what was the final exam score for each student?

## Expert Answers (1)

2021-05-19
Given: μ= 150
σ=20
The final exam scoreis the mean increased by the product of the z-score and the standard deviation, since the z-score measures the number of standard devintions that the value is from the mean:
Robert: x = μ + zσ = 150 + 1.10(20) = 172
Joel: x = μ + zσ = 150 + 0.00(20) = 150
Juan: x = μ + zσ = 150 + 1.70(20) = 184
Jan: x = μ + zσ = 150 — 0.80(20) = 134
Susan: x = μ + zσ = 150 — 2.00(20) = 110
Linda: x = μ + zσ = 150 + 1.60(20) = 182

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