Question: For a normal distribution, use the given z-scores to find the requested probability:
Probability is greater than or equal to a z score of 2.
I drew a distribute (picture this: the mean of 0 set at the middle and a line drawn at 2 shaded to the right).
But how do I go about finding the area of the shaded region?
The table reads "less than" so you do 1 - (the z-score table value corresponding to 2)
use the z-score table to find the portion of the population below 2
the number should be something like .9772
the probability of a z-score above this is ... 1 - .9772
To find the probability for a given z-score in a normal distribution, you can use a standard normal distribution table or a statistical software. Here are the steps to find the probability of a z-score greater than or equal to 2 using a standard normal distribution table:
1. Look up the z-score of 2 in the table. The table will provide you with the area under the curve to the left of the z-score.
2. Since you want the probability of the z-score greater than or equal to 2, subtract the area you obtained from the table from 1 (the total area under the curve).
For example, when you look up the z-score of 2 in the table, you might find that the area to the left of 2 is 0.9772. Subtracting this from 1, you would get 1 - 0.9772 = 0.0228. This means that the probability of having a z-score greater than or equal to 2 is 0.0228, or 2.28%.
If you have access to statistical software like Excel or Python, you can also use functions like NORM.S.DIST or scipy.stats.norm.sf to directly calculate the probability without the need for a table.