for a normal population with m=100 and s=20, what is the probability of obtaining a score greater than 108?
To find the probability of obtaining a score greater than 108 in a normal population with a mean (μ) of 100 and a standard deviation (σ) of 20, we need to calculate the z-score first.
The z-score formula is: z = (x - μ) / σ
Where:
x = the value we want to find the probability for
μ = the population mean
σ = the standard deviation
Plugging in the values, we have:
z = (108 - 100) / 20
z = 8 / 20
z = 0.4
Now, we need to find the area (probability) to the right of this z-score on the standard normal distribution table. This will give us the probability of obtaining a score greater than 108.
Using a standard normal distribution table or a calculator, we can find that the area to the left of z = 0.4 is approximately 0.6554.
Since we want the area to the right of z = 0.4, we subtract the area to the left from 1 to get the area to the right:
1 - 0.6554 = 0.3446
Therefore, the probability of obtaining a score greater than 108 is approximately 0.3446 or 34.46%.