Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 4.8. If one ACT score is randomly selected, find the probability that it is greater than 20.

Find the z-score.

http://www.ehow.com/how_4555631_calculate-zscore-statistics.html

Then look up the p value on the z table.

To find the probability that a randomly selected ACT score is greater than 20, we need to calculate the area under the normal distribution curve to the right of 20.

Step 1: Standardize the score
To standardize the score, we use the formula:
standardized score (z) = (x - mean) / standard deviation

In this case, the score we are interested in is 20, the mean is 21.1, and the standard deviation is 4.8.
So, plugging in the values:
z = (20 - 21.1) / 4.8 = -0.2292

Step 2: Find the probability
We need to find the area under the normal distribution curve to the right of -0.2292.
This can be done using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we find the corresponding value for -0.2292, which is 0.4107. This value represents the area to the left of -0.2292 on the standard normal distribution curve.

Since we want the probability to the right of 20, we subtract the value obtained from 1:
Probability = 1 - 0.4107 = 0.5893

Therefore, the probability that a randomly selected ACT score is greater than 20 is approximately 0.5893 or 58.93%.