Find the area of the shaded region under the standard distribution curve.
(I can’t add a picture)
Z=-9.0
Z=1.60
Does your problem give you an equation for the curve?
You can play around with Z-table stuff here:
http://davidmlane.com/hyperstat/z_table.html
To find the area of the shaded region under the standard distribution curve between the z-scores -9.0 and 1.60, we can use a standard normal distribution table or a statistical software.
Using a standard normal distribution table:
1. For the z-score of -9.0, we can look up the area to the left of this z-score in the table. However, since the table typically only contains values up to a z-score of 3.99, it's safe to assume that the area to the left of -9.0 is virtually 0.
2. For the z-score of 1.60, we can look up the area to the left of this z-score in the table. The table will give us a value of approximately 0.9452.
3. To find the shaded area between -9.0 and 1.60, we subtract the smaller area from the larger area:
Area = 0.9452 - 0 ≈ 0.9452
Therefore, the area of the shaded region under the standard distribution curve between z-scores -9.0 and 1.60 is approximately 0.9452.
To find the area of the shaded region under the standard distribution curve, we first need to determine the values of the cumulative distribution function (CDF) at the given z-scores. The CDF represents the probability of a standardized random variable being less than or equal to a given value.
Unfortunately, the z-score value of -9.0 is extremely low and doesn't exist in standard normal distribution tables, as the standard normal distribution table typically provides values up to roughly z = 3. However, we can still determine the area under the curve using the properties of the standard normal distribution.
For a z-score of -9.0, we know that the corresponding area under the curve will be extremely close to 0. It practically means that the shaded region is nearly non-existent and can be considered negligible.
On the other hand, for a z-score of 1.60, we can determine the area under the curve by finding the cumulative probability corresponding to that z-score.
Using the standard normal distribution table or statistical software, we can find that the cumulative probability for a z-score of 1.60 is approximately 0.9452.
Since the area under the entire standard normal distribution curve is equal to 1, the area of the shaded region under the curve for a z-score of 1.60 can be calculated by subtracting the cumulative probability from 1:
Area = 1 - 0.9452 = 0.0548
Therefore, the area of the shaded region under the standard distribution curve for a z-score of 1.60 is approximately 0.0548 or 5.48%.