Given $X=45.5, \mu=40$, and $\sigma=2$, indicate on the curve where the given $X$ value would be.
Answer
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Step 1 ：The problem is asking to find the position of a given value on a normal distribution curve. The normal distribution curve is defined by its mean (μ) and standard deviation (σ). The given value X is 45.5, the mean (μ) is 40 and the standard deviation (σ) is 2.

Step 2 ：The position of X on the curve can be found by calculating the z-score. The z-score is a measure of how many standard deviations an element is from the mean. It is calculated as follows: \(z = \frac{X - μ}{σ}\)

Step 3 ：Substitute the given values into the z-score formula: \(z = \frac{45.5 - 40}{2}\)

Step 4 ：Calculate the z-score: \(z = 2.75\)

Step 5 ：The z-score of 2.75 indicates that the given value X=45.5 is 2.75 standard deviations above the mean. This is the position of X on the normal distribution curve.

Step 6 ：Final Answer: The given value \(X=45.5\) would be at the position corresponding to a z-score of \(\boxed{2.75}\) on the curve.