P (-1.1 ¡Ü Z ¡Ü 0)
the symbols are less than or equal to
If you look up a standard normal distribution table for Z, you will find that P(-1.1<Z<0)
= Z(0)-Z(-1.1)
= 0 - (-.3643)
= 0.3643
To find the probability P(-1.1 ≤ Z ≤ 0), you can use a standard normal distribution table or a calculator that can compute the cumulative distribution function (CDF) for the standard normal distribution.
The standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1. It is also sometimes referred to as the Z distribution.
Here's how you can use a standard normal distribution table to find the probability:
1. Look up the value for -1.1 in the body of the table. In this case, you may need to find the closest value to -1.1, for example, -1.09 or -1.10. Let's assume you find -1.10 in the table.
2. Look up the value for 0 in the body of the table. The value for 0 in the standard normal distribution table is typically at the center since the standard deviation is 1.
3. Subtract the value from step 1 from the value from step 2. In this case, you would subtract the value for -1.10 from the value for 0. For example, if the value for -1.10 is 0.1357 and the value for 0 is 0.5, you would calculate 0.5 - 0.1357 = 0.3643.
4. The result from step 3 represents the probability P(-1.1 ≤ Z ≤ 0). In this case, the probability P(-1.1 ≤ Z ≤ 0) is approximately 0.3643 or 36.43%.
Alternatively, you can use a calculator with a standard normal distribution function to find the probability directly. Most statistical or scientific calculators have this function built-in. Just input the lower and upper limits (-1.1 and 0 in this case) along with the mean (0) and standard deviation (1) of the standard normal distribution, and it will give you the probability directly.