Question

question
nathaniel earned a score of 675 on exam a that had a mean of 650 and a standard deviation of 25. he is about to take exam b that has a mean of 21 and a standard deviation of 4. how well must nathaniel 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.
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Explanation:

Step1: Calculate z-score for Exam A

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x$ is the raw score, $\mu$ is the mean, and $\sigma$ is the standard deviation.
For Exam A: $x=675$, $\mu=650$, $\sigma=25$.
$z = \frac{675 - 650}{25} = \frac{25}{25} = 1$

Step2: Use z-score to find Exam B score

Rearrange the z-score formula to solve for $x$: $x = z\sigma + \mu$.
For Exam B: $z=1$, $\mu=21$, $\sigma=4$.
$x = (1)(4) + 21 = 4 + 21 = 25$

Answer:

25