Answer:
86
Step-by-step explanation:
Mean scores of first test = ![u_{1}=23](https://tex.z-dn.net/?f=u_%7B1%7D%3D23)
Standard deviation of first test scores = ![\sigma_{1} =4.2](https://tex.z-dn.net/?f=%5Csigma_%7B1%7D%20%3D4.2)
Mean scores of second test = ![u_{2}=71](https://tex.z-dn.net/?f=u_%7B2%7D%3D71)
Standard deviation of second test scores = ![\sigma_{2} =10.8](https://tex.z-dn.net/?f=%5Csigma_%7B2%7D%20%3D10.8)
We have to find if a student scores 29 on his first test, what will be his equivalent score on the second test. The equivalent scores must have the same z-scores. So we have to find the z-score from 1st test and calculate how much scores in second test would result in that z-score.
The formula for z-score is:
![z=\frac{x-u}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-u%7D%7B%5Csigma%7D)
Calculating the z-score for the 29 scores in first test, we get:
![z=\frac{29-23}{4.2}=1.43](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B29-23%7D%7B4.2%7D%3D1.43)
This means, the equivalent scores in second test must have the same z-scores.
i.e for second test:
![1.43=\frac{x-71}{10.8}\\\\ x-71 = 15.444\\\\ x = 86.444](https://tex.z-dn.net/?f=1.43%3D%5Cfrac%7Bx-71%7D%7B10.8%7D%5C%5C%5C%5C%20x-71%20%3D%2015.444%5C%5C%5C%5C%20x%20%3D%2086.444)
Rounding of to nearest integer, the equivalent scores in the second test would be 86.