Question

question 4 of 10. step 1 of 1
calculate the standard score of the given x value, x = 95.8, where μ = 89.7 and σ = 87.7. round your answer to two decimal places.
answer
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Explanation:

Step1: Recall standard - score formula

The formula for the standard score (z - score) is $z=\frac{X-\mu}{\sigma}$, where $X$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Substitute given values

Substitute $X = 95.8$, $\mu=89.7$, and $\sigma = 87.7$ into the formula: $z=\frac{95.8 - 89.7}{87.7}$.

Step3: Calculate the numerator

$95.8−89.7 = 6.1$. So, $z=\frac{6.1}{87.7}$.

Step4: Calculate the z - score

$z=\frac{6.1}{87.7}\approx0.07$.

Answer:

$0.07$