5Z: Topics in Math; Pirnot 6ed.
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Assume that math test scores are normally distributed with a mean of 200 and a sthidard deviation of 40 . If you were to score 120 on this exam, what percentage of those taking the test scored below you?
Click the icon to view the table of $z$ -scores.

What percentage of those taking the test scored below you?
$◻ %$
(Round to the nearest tenth as needed.)

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$2.3 %$ (rounded to the nearest tenth) of those taking the test scored below you.

Steps

Step 1 ：Calculate the z-score using the formula: $Z = \frac{X - μ}{σ}$

Step 2 ：Substitute the given values into the formula: $Z = \frac{120 - 200}{40} = - 2$

Step 3 ：A z-score of -2 means that the test score of 120 is 2 standard deviations below the mean.

Step 4 ：Use a z-table to find the percentage of test scores that fall below a z-score of -2. The z-table shows that approximately 2.28% of test scores fall below this value.

Step 5 ： $2.3 %$ (rounded to the nearest tenth) of those taking the test scored below you.

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