A set of data is normally distributed with a mean of 98 and a standard deviation of 15. What is the probability that the value from the data is less than 88 ?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
To solve this question, we need to find the area under the normal distribution curve to the left of the value 88.
First, let's standardize the value 88 using the formula for standardization:
z = (x - mean) / standard deviation
where x is the value we want to find the probability for, mean is the mean of the distribution, and standard deviation is the standard deviation of the distribution.
In this case:
z = (88 - 98) / 15 = -10 / 15 = -0.67
Next, we need to find the cumulative probability associated with the z-score -0.67. We can do this by looking up the z-score in a standard normal distribution table or by using a calculator.
Using the z-table, we can find that the cumulative probability associated with a z-score of -0.67 is approximately 0.2514.
So, the probability that a value from the data is less than 88 is approximately 0.2514 or 25.14%.