Respuesta :
Using z-scores, it is found that he must score 550 on Exam B order to do equivalently well as he did on Exam A.
What is the z-score formula?
The z-score of a measure X of a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean.
For Exam A, we have that the parameters are [tex]X = 610, \mu = 650, \sigma = 40[/tex], hence his grade had a z-score given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{610 - 650}{40}[/tex]
[tex]Z = -1[/tex]
In Exam B, with [tex]\mu = 600, \sigma = 50[/tex], we want the grade X with the same z-score of Z = -1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1 = \frac{X - 600}{50}[/tex]
X - 600 = -50
X = 550.
He must score 550 on Exam B order to do equivalently well as he did on Exam A.
More can be learned about z-scores at https://brainly.com/question/24663213
