Question

Aiden earned a score of 22 on exam a that had a mean of 40 and a standard
deviation of 10. he is about to take exam b that has a mean of 650 and a standard
deviation of 25. how well must aiden score on exam b in order to do equivalently
well as he did on exam a? assume that scores on each exam are normally distributed.

Answer 1

Using the normal distribution, it is found that he needs a score of 605 in exam b in order to do equivalently well as he did on exam a.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

For the z-score for exam a, we have that the parameters are given as follows:

$X = 22, \mu = 40, \sigma = 10$

Hence:

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

$Z = \frac{22 - 40}{10}$

Z = -1.8.

Then, for the equivalent grade X in exam B, we have that:

$Z = -1.8, \mu = 650, \sigma = 25$

Then:

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

$-1.8 = \frac{X - 650}{25}$

X - 650 = -1.8 x 25

X = 605.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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