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Question Find the score in the 70th percentile of a dataset with mean μ=79.22\mu=79.22 and standard deviation σ=7.97\sigma=7.97 using the Z-score formula Z=X−μσZ = \frac{X - \mu}{\sigma}.

Studdy Solution

STEP 1

Assumptions1. The mean of the dataset is79.22. The standard deviation of the dataset is7.973. We are looking for the Z-score that represents the70th percentile4. The Z-score is calculated using the formula Z=X−μσZ = \frac{X - \mu}{\sigma}

STEP 2

First, we need to find the Z-score that corresponds to the70th percentile. In a standard normal distribution, the70th percentile corresponds to a Z-score of approximately0.52. This value can be found in a standard Z-score table or calculated using statistical software.

STEP 3

Now that we have the Z-score, we can plug this into the Z-score formula and solve for XX, the score in the70th percentile.
0.52=X−79.227.970.52 = \frac{X -79.22}{7.97}

STEP 4

First, multiply both sides of the equation by the standard deviation,7.97.
0.52×7.97=X−79.220.52 \times7.97 = X -79.22

STEP 5

Calculate the left side of the equation.
4.14=X−79.224.14 = X -79.22

STEP 6

Next, add the mean,79.22, to both sides of the equation to solve for XX.
4.14+79.22=X4.14 +79.22 = X

STEP 7

Calculate the right side of the equation.
83.36=X83.36 = XThe score that represents the70th percentile in the dataset is approximately83.36.

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