Question

Avery earned a score of 310 on Exam A that had a mean of 350 and a standard deviation of 20. She is about to take Exam B that has a mean of 550 and a standard deviation of 40. How well must Avery score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally disturbed.

Answer 1

The score that Avery must get on Exam B is given as follows:

470.

What is the z-score formula?

The z-score of a measure X of a variable that has mean symbolized by $\mu$ and standard deviation symbolized by $\sigma$ is obtained by the rule presented as follows:

$Z = \frac{X - \mu}{\sigma}$

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.

For exam A, the mean and the standard deviation are given as follows:

$\mu = 350, \sigma = 20$

She scored 310, hence the z-score of her grade is given as follows:

Z = (310 - 350)/20

Z = -2.

For exam B, the mean and the standard deviation are given as follows:

$\mu = 550, \sigma = 40$

To do as well as on exam A, she needs a z-score of -2, hence the grade X is obtained as follows:

-2 = (X - 550)/40

X - 550 = -80

X = 470.

More can be learned about the normal distribution at https://brainly.com/question/25800303

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