Question

Given X=72.8 X = 72.8 , μ=66.5 μ = 66.5 , and σ=3.5 σ = 3.5 ,

indicate on the curve where the given X value would be.

Answer 1

To indicate where the given X value would be on the curve, calculate the z-score using the formula Z = (X - μ) / σ. With a z-score of 1.8, the given X value of 72.8 would be located to the right of 96.41% of the distribution curve.

Step-by-step explanation:

Given X = 72.8, μ = 66.5, and σ = 3.5, we can use the concept of z-scores to indicate where the given X value would be on the curve. The formula for calculating the z-score is Z = (X - μ) / σ.

Plugging in the values, we get Z = (72.8 - 66.5) / 3.5 = 1.8.

With a z-score of 1.8, we can refer to a z-table to find the corresponding area under the normal distribution curve. From the table, we can see that the area to the left of 1.80 is approximately 0.9641, or 96.41%.

This means that the given X value of 72.8 would be located to the right of 96.41% of the distribution curve.