Question

Annie was told that her math test score was 3 standard deviations below the mean. If test scores were approximately normal with μ=99 and σ=4, what was Annie's score? Do not include units in your answer. For example, if you found that the score was 99 points, you would enter 99.

Answer 1

Answer: 87

Explanation:

We can work backwards using the z-score formula to find the x-value. The problem gives us the values for z, μ and σ. So, let's substitute these numbers back into the formula:

z−3−1287=x−μσ=x−994=x−99=x

We can think of this conceptually as well. We know that the z-score is −3, which tells us that x is three standard deviations to the left of the mean, 99. So we can think of the distance between 99 and the x-value as (3)(4)=12. So Annie's score is 99−12=87.

Answer 2

`X \sim N(99,4)`

Where
`\mu=99` and
`\sigma=4`

We want to find the Annie's score takign in count that the score is 3 deviations below the mean, so then we can find the value with this formula:

`X = \mu -3\sigma`

And replacing we got:

`X = 99 -3*4 = 87`

So then the Annie's score would be 87

Explanation:

Let X the random variable that represent the test scores of a population, and for this case we know the distribution for X is given by:

`X \sim N(99,4)`

Where
`\mu=99` and
`\sigma=4`

We want to find the Annie's score takign in count that the score is 3 deviations below the mean, so then we can find the value with this formula:

`X = \mu -3\sigma`

And replacing we got:

`X = 99 -3*4 = 87`

So then the Annie's score would be 87