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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?

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

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To find the area between two values in a normal distribution, you can use a standard normal distribution table or calculate it using a statistical calculator. Here's how you can use the table to solve these problems:

1. Finding the area between 415 pounds and the mean of 400 pounds:

Step 1: Standardize the values using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
For the value 415 pounds:
z = (415 - 400) / 10
z = 1.5

Step 2: Look up the area corresponding to the standardized z-value.
Referring to the standard normal distribution table, the area to the left of z = 1.5 is approximately 0.9332.

Step 3: Subtract the area to the left of the lower value from the area to the left of the higher value.
The area between 415 pounds and the mean of 400 pounds is approximately 0.9332 - 0.5 = 0.4332.

2. Finding the area between the mean and 395 pounds:

Step 1: Standardize the values:
For the value 395 pounds:
z = (395 - 400) / 10
z = -0.5

Step 2: Look up the area corresponding to the standardized z-value.
Referring to the standard normal distribution table, the area to the left of z = -0.5 is approximately 0.3085.

Step 3: Since the lower value is to the left of the mean, subtract the area to the left of the lower value from the area to the left of the higher value.
The area between the mean of 400 pounds and 395 pounds is approximately 0.5 - 0.3085 = 0.1915.

Alternatively, you can also use a statistical calculator or software to find these areas directly by entering the mean, standard deviation, and the values you want to calculate the area between.