QuestionFind the z-score for a score of 350 on a normal distribution with mean 300 and standard deviation 40.

Studdy Solution

STEP 1

Assumptions1. The scores on the exam are normally distributed. The mean score is3003. The standard deviation is404. The score of the person in question is350

STEP 2

The z-score is a measure of how many standard deviations an element is from the mean. It can be calculated using the following formula $z = \frac{X - \mu}{\sigma}$ where- $X$ is the score of the person, - $\mu$ is the mean score, and- $\sigma$ is the standard deviation.

STEP 3

Now, plug in the given values for the score of the person, the mean score, and the standard deviation into the formula to calculate the z-score.
$z = \frac{350 -300}{40}$

STEP 4

First, subtract the mean score from the score of the person.
$z = \frac{50}{40}$

STEP 5

Finally, divide the result by the standard deviation to find the z-score.
$z = \frac{50}{40} =1.25$ The z-score of the person who scored350 on the exam is1.25.

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