Final answer:
The probability that x falls within the shaded area can be calculated using z-scores and standard normal distribution tables, statistical software, or calculators, with methods differing based on the type of distribution. For a normal distribution, use functions such as normalcdf. For a uniform distribution, calculate the area of the shaded rectangle.
Step-by-step explanation:
To find the probability that x falls within the shaded area on a graph, you need to consider the nature of the distribution and use the appropriate method to calculate the area under the curve. If the distribution is normal, you would use z-scores and standard normal distribution tables, or a statistical software or calculator capable of performing these calculations, such as the normalcdf function mentioned.
As an example, if you are asked to find the probability P(85< x <92), and given that P(85< x <92) = 0.6997, it indicates that the probability that x is between 85 and 92 is approximately 0.6997, or 69.97%. To visualize this, sketch a graph of the distribution and shade the area between x = 85 and x = 92. This shaded region represents the desired probability.
If the distribution is not normal or if you have a uniform distribution where the height of the distribution is constant across the range of x, the area (and hence the probability) between two points on the x-axis is simply the base times the height of the rectangle formed by those two points. For instance, to find P(3 < x < 6), sketch a graph, shade the region between x = 3 and x = 6, and calculate the area of that rectangle to determine the probability.