Respuesta :
Answer:Calculus
Step-by-step explanation:
Given
Chemistry score are normally distributed with a mean score of 75 and standard deviation 12
[tex]\mu _1=75[/tex]
[tex]\sigma _1=12[/tex]
Calculus score
[tex]\mu _2=80[/tex]
[tex]\sigma _2=8[/tex]
For chemistry
[tex]z=\frac{81-75}{12}=0.4167\approx 0.42[/tex]
For calculus
[tex]z=\frac{84-80}{8}=0.5[/tex]
From Z score it is clear that student score better marks in calculus.
Using z-scores, it is found that due to equal z-scores, the student performed the same relative to the classes in each subject.
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Z-score:
- In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The Z-score measures how many standard deviations the measure is from the mean.
- Relative to the respective class, the student did better in the discipline in which his grade had a higher z-score.
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Chemistry:
- Mean of 75 means that [tex]\mu = 75[/tex]
- Standard deviation of 12 means that [tex]\sigma = 12[/tex]
- Grade of 81 means that [tex]X = 81[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{81 - 75}{12}[/tex]
[tex]Z = 0.5[/tex]
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Calculus:
- Mean of 80 means that [tex]\mu = 80[/tex]
- Standard deviation of 8 means that [tex]\sigma = 8[/tex]
- Grade of 84 means that [tex]X = 84[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{84 - 80}{8}[/tex]
[tex]Z = 0.5[/tex]
Due to equal z-scores, the student performed the same relative to the classes in each subject.
A similar problem is given at https://brainly.com/question/23530266
