Consider a normal distribution with mean 20 and standard deviation 3. What is the probability a value selected at random from this distribution is greater than 20?
50%
To find the probability that a value selected at random from a normal distribution is greater than 20, we need to find the area under the curve to the right of the value 20.
First, we need to standardize the value 20 using the formula: z = (x - μ) / σ, where x is the value (in this case, 20), μ is the mean (20), and σ is the standard deviation (3).
Using the formula, we can calculate the z-score:
z = (20 - 20) / 3 = 0 / 3 = 0
Since we are looking for the area to the right of 20, we need to find the area under the normal curve to the right of the z-score 0.
We can use a standard normal distribution table or calculator to find this area.
Using a standard normal distribution table or calculator, we find that the area to the right of the z-score 0 is approximately 0.5000.
Therefore, the probability that a value selected at random from this normal distribution is greater than 20 is 0.5000, or 50%.
5.2
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
OR… what is the probability of being higher than the mean in a normal distribution?