IQ scores distribution of IQ scores is normally distributed

standard with a mean of 100 and a standard deviation of 15, which is represented by a bell-shaped graphical.
What is the area under the curve?
What is the median?
What is the mode?

Yes, you can find the answers if the distribution curve is known.

The standard normal distribution curve has an area of 1.0 under the curve.
To convert a curve with mean 100 and SD=15 to the normal curve, we use
Z(X)=(X-μ)/σ
which means
X=σZ(X)+μ
where σ=15 and μ=100.

Translation of a curve does not change the area, but scaling it modifies the area by the multiplicative factor.

Hints for second and third part:
All symmetrical probability distribution curves such as the Normal distribution curve have identical mean/median/mode.

To answer these questions, we need to understand the properties of a normal distribution.

1. Area under the curve: The area under the curve represents the probability of a certain event occurring. In a normal distribution, the total area under the curve is always equal to 1 or 100%. This means that the probability of obtaining any value within the distribution is 1.

2. Median: The median is the value that separates the distribution into two equal halves. In a normal distribution, the median is equal to the mean, which in this case is 100. This implies that 50% of the population have IQ scores below 100, and 50% have IQ scores above 100.

3. Mode: The mode is the value that occurs with the highest frequency in the distribution. In a normal distribution, the mode is the same as the peak or highest point on the bell-shaped curve. In this case, the mode cannot be determined based solely on the mean and standard deviation provided.

However, it is important to note that in a perfectly symmetrical normal distribution, the mean, median, and mode will all be equal. But within the given information, we cannot specifically determine the mode.

To further calculate specific probabilities or analyze the distribution, we can use the properties of the standard normal distribution and z-scores.