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Alice was told that her reading test score was 2 standard deviations below the mean. If test scores were approximately normal with [tex]\mu=80[/tex] and [tex]\sigma=3[/tex], what was Alice's score? Do not include units in your answer. For example, if you found that the score was 86 points, you would enter 86.

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Answer :

GinnyAnswer
To determine Alice's reading test score, we need to account for her score being 2 standard deviations below the mean of the test scores. We are given the following information:

- The mean score [tex]\(\mu\)[/tex] is 80.
- The standard deviation [tex]\(\sigma\)[/tex] is 3.
- Alice's score is 2 standard deviations below the mean.

Here is the step-by-step calculation:

1. Calculate the total amount by which Alice's score is below the mean:
[tex]\(2 \times \sigma = 2 \times 3 = 6\)[/tex].

2. Subtract this value from the mean to find Alice's score:
[tex]\(\mu - 6 = 80 - 6 = 74\)[/tex].

Therefore, Alice's score is [tex]\(74\)[/tex].

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