Answer:
Wyatt must get a score of 150 on Exam B in order to do equivalently well as he did on Exam A.
Step-by-step explanation:
Let's calculate the test statistic of each score based on the mean and standard deviation of each test.
This statistic will show us how far from the mean, measured in standard deviations, Wyatt's test score is.
The formula for the test statistic is:
- [tex]\displaystyle Z = \frac{x- \mu}{\sigma}[/tex]
- x = observed value
- [tex]\mu[/tex] is the population mean
- [tex]\sigma[/tex] is the population standard deviation
Let's calculate the test statistic for each test.
Exam A:
- [tex]\displaystyle Z = \frac{45-35}{5} = \frac{10}{5}= 2[/tex]
Exam B:
- [tex]\displaystyle Z = \frac{x-100}{25}[/tex]
Since we want the test statistic to be the same for both exam A and exam B, let Z = 2 and solve for x for Exam B.
- [tex]\displaystyle 2 = \frac{x-100}{25} \\ 50 = x - 100 \\ x = 150[/tex]
Wyatt must get a score of 150 on Exam B in order to do equivalently well as he did on Exam A. This score means that Wyatt is 2 standard deviations from the mean score on Exam B as he scored on Exam A.
