Question

Assume that minutes engaged in aerobic activity in a population is normally distributed with mean= 20 and variance=20

kg/m?. What is the area under the curve below 15?

Answer 1

To find the area under the curve below a certain value, you can use the cumulative distribution function (CDF) of the normal distribution.

First, let's calculate the standard deviation (σ) using the variance (σ^2):

Standard Deviation (σ) = √Variance = √20 = 4.47

Next, we use the Z-score formula to convert the given value (15) into a standardized score:

Z = (x - μ) / σ

where x is the given value, μ is the mean, and σ is the standard deviation.

Z = (15 - 20) / 4.47 ≈ -1.118

Now, we need to find the area to the left of this Z-score on the standard normal distribution.

Using a standard normal distribution table or a calculator, you can find the area corresponding to the Z-score -1.118, which is approximately 0.1314.

Therefore, the area under the curve below 15 is approximately 0.1314 or 13.14%.