Answer:
86
Step-by-step explanation:
Mean scores of first test = [tex]u_{1}=23[/tex]
Standard deviation of first test scores = [tex]\sigma_{1} =4.2[/tex]
Mean scores of second test = [tex]u_{2}=71[/tex]
Standard deviation of second test scores = [tex]\sigma_{2} =10.8[/tex]
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:
[tex]z=\frac{x-u}{\sigma}[/tex]
Calculating the z-score for the 29 scores in first test, we get:
[tex]z=\frac{29-23}{4.2}=1.43[/tex]
This means, the equivalent scores in second test must have the same z-scores.
i.e for second test:
[tex]1.43=\frac{x-71}{10.8}\\\\ x-71 = 15.444\\\\ x = 86.444[/tex]
Rounding of to nearest integer, the equivalent scores in the second test would be 86.
