117k views
0 votes
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?

1 Answer

3 votes
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%.
User Goralight
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories