The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? The area between the mean and 395?

Hmmm. Area? or do you mean the probability? The area under a probability density function is area, so you have a probabliity density x deviation which equals probability. The entire area is 1.00 under the function.

See this applet:http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html

The area under the curve indicates the probability. Use the Z-score to determine area.

Z = (x - μ )/SD, where x = score, μ = mean, and SD = standard deviation.

Use table in your statistics text called "areas under normal distribution" or the source indicated by bobpursley to get the area from the Z-score.

I hope this helps a little more. Thanks for asking.

To find the area between two points on a normal distribution curve, we need to calculate the z-scores for those points and then use a standard normal distribution table or calculator to find the corresponding areas.

To find the z-score for 415 pounds:
z = (x - μ) / σ
where x is the value (415), μ is the mean (400), and σ is the standard deviation (10).

z = (415 - 400) / 10
z = 15 / 10
z = 1.5

To find the z-score for 395 pounds:
z = (x - μ) / σ
where x is the value (395), μ is the mean (400), and σ is the standard deviation (10).

z = (395 - 400) / 10
z = -5 / 10
z = -0.5

Using a standard normal distribution table or calculator, we can find the area corresponding to each z-score.

The area between 415 pounds and the mean of 400 pounds is the area to the right of the z-score 1.5 (since it is greater than the mean) minus the area to the right of the z-score -0.5.

Area = (Area to the right of 1.5) - (Area to the right of -0.5)

Using a standard normal distribution table or calculator, we find:
Area to the right of 1.5 = 0.0668
Area to the right of -0.5 = 0.3085

Area = 0.0668 - 0.3085
= -0.2417

However, it isn't possible to have a negative area, so the calculated area must be a mistake in the calculation. Please double-check the values or the question.

Similarly, the area between the mean of 400 pounds and 395 pounds is the area to the right of the z-score -0.5.

Area = Area to the right of -0.5

Using a standard normal distribution table or calculator, we find:
Area to the right of -0.5 = 0.3085

To find the areas between two values in a normal distribution, we can use the standard normal distribution table or calculate the z-scores.

The z-score indicates how many standard deviations a value is from the mean. It can be calculated using the following formula:

z = (x - μ) / σ

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

Let's calculate the z-scores for the given values:

For 415 pounds:
z1 = (415 - 400) / 10 = 1.5

For 395 pounds:
z2 = (395 - 400) / 10 = -0.5

Now, we need to find the area between these two z-scores using the standard normal distribution table or a statistical software.

Using the standard normal distribution table:
Look up the cumulative probability for each z-score.

For z1 = 1.5, the cumulative probability is 0.9332
For z2 = -0.5, the cumulative probability is 0.3085

To find the area between the two values, subtract the lower cumulative probability from the higher cumulative probability:

Area between 415 pounds and the mean of 400 pounds = 0.9332 - 0.3085 = 0.6247

Area between the mean and 395 pounds = 1 - Area between 415 pounds and the mean of 400 pounds = 1 - 0.6247 = 0.3753

Therefore, the area between 415 pounds and the mean of 400 pounds is approximately 0.6247, and the area between the mean and 395 pounds is approximately 0.3753.