Math

QuestionFind the proportion of SAT verbal scores between 200 and 800800 using the zz distribution. Choices: .3413, .2500, .5000, .9970.

Studdy Solution

STEP 1

Assumptions1. The SAT verbal scores follow a standard normal distribution (z distribution). . The scores we are interested in are between200 and800.
3. There is no given average, so we assume the mean to be0 and the standard deviation to be1, as is standard for the z distribution.

STEP 2

First, we need to convert the scores to z-scores. The z-score is calculated by subtracting the mean from the value and dividing by the standard deviation. Since we are assuming a standard normal distribution, the mean is0 and the standard deviation is1.
z=Xμσz = \frac{X - \mu}{\sigma}

STEP 3

Plug in the values for the scores, the mean, and the standard deviation to calculate the z-scores.
For200z200=20001=200z_{200} = \frac{200 -0}{1} =200For800z800=80001=800z_{800} = \frac{800 -0}{1} =800

STEP 4

The proportion of scores between200 and800 is the area under the curve of the z distribution between these two z-scores. This is found by subtracting the cumulative distribution function (CDF) value of the lower z-score from the CDF value of the higher z-score.
Proportion=CDF(z800)CDF(z200)Proportion = CDF(z_{800}) - CDF(z_{200})

STEP 5

However, the z-scores we have calculated are not realistic for a standard normal distribution, which typically has z-scores between -3 and3. This is because the SAT scores do not actually have a mean of0 and a standard deviation of1. Without the actual mean and standard deviation, we cannot calculate the exact z-scores or the proportion of scores between200 and800.
Therefore, we cannot solve this problem with the given information. The question seems to be flawed as it doesn't provide necessary information to solve it.

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