Math

QuestionFind the proportion of scores in a zz distribution between z=0.00z = 0.00 and z=2.00z = 2.00. Options: .3413, .4772, .7500, .8176.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a standard normal distribution (z-distribution). . The z-scores given are0.00 and.00.
3. We need to find the proportion of scores that fall between these two z-scores.

STEP 2

To solve this problem, we need to understand that the area under the curve of a standard normal distribution represents the proportion of scores. The total area under the curve is1, or100%.

STEP 3

The z-score of0.00 corresponds to the mean of the distribution. In a standard normal distribution,50% of the scores fall below the mean and50% above. Therefore, the proportion of scores below a z-score of0.00 is0.5 or50%.

STEP 4

To find the proportion of scores below a z-score of2.00, we refer to a z-table or use a statistical software. The value corresponding to a z-score of2.00 is approximately0.9772. This means that about97.72% of the scores fall below a z-score of2.00.

STEP 5

To find the proportion of scores that fall between a z-score of0.00 and a z-score of2.00, we subtract the proportion of scores below a z-score of0.00 from the proportion of scores below a z-score of2.00.
Proportion=Proportionz=2.00Proportionz=0.00Proportion = Proportion_{z=2.00} - Proportion_{z=0.00}

STEP 6

Plug in the values for the proportions to calculate the proportion of scores between the two z-scores.
Proportion=0.97720.5Proportion =0.9772 -0.5

STEP 7

Calculate the proportion of scores between the two z-scores.
Proportion=0.97720.5=0.4772Proportion =0.9772 -0.5 =0.4772So, the proportion of scores on a z distribution that fall between a z score of0.00 and a z score of2.00 is0.4772 or47.72%.

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