P (-1.1 <_ Z <_ 0)
the symbols are less than or equal to but i can't make them on here
Use the webpage I gave you,
click on "between"
This inequality means that Z can vary
from -1.1 to 0. Therefore, Z=-1.1min.
Z=0,max.
To find the probability of Z falling between -1.1 and 0, you will need to use a standard normal distribution table or a statistical calculator that can provide you with the area under the standard normal curve.
Here's how you can find the probability step by step:
1. Subtract the mean, μ, from the upper and lower bounds of the interval to standardize the interval in terms of the standard deviation.
For the lower bound, z1, we have:
z1 = (-1.1 - μ) / σ
For the upper bound, z2, we have:
z2 = (0 - μ) / σ
Here, μ represents the mean of the standard normal distribution, and σ represents the standard deviation.
2. Look for the values of z1 and z2 in the standard normal distribution table. These tables provide the probabilities for various z-scores.
3. Find the area under the curve between z1 and z2. Depending on the format of the table, you may need to perform some calculations. One common method is to find the probability corresponding to z1 and subtract the probability corresponding to z2. This will give you the probability of Z falling between -1.1 and 0.
Alternatively, if you are using a statistical calculator, you can input the values of z1 and z2 directly and it will provide you with the probability.
Remember, the standard normal distribution table provides the probability for Z being less than a given value. Therefore, you may need to subtract the probability corresponding to z1 from the probability corresponding to z2 to get the probability between the two values.
I hope this explanation helps you understand how to find the probability for a range of values using a standard normal distribution table or a statistical calculator.