Step-by-step explanation:
It seems like the end of your question got cut off. If you meant to ask for the probability \( P(X < 8) \), we can calculate that using the standard normal distribution with the given mean and standard deviation.
Given:
Mean (\(\mu\)) = 10
Standard Deviation (\(\sigma\)) = 2
To find \( P(X < 8) \), we'll use the Z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.
First, calculate the Z-score:
\[ Z = \frac{X - \mu}{\sigma} \]
\[ Z = \frac{8 - 10}{2} = \frac{-2}{2} = -1 \]
Using the standard normal distribution table (or calculator), find the probability corresponding to \( Z = -1 \). The probability of \( P(X < 8) \) is the probability to the left of the Z-score -1.
Consulting the standard normal distribution table, the probability for \( Z = -1 \) is approximately 0.1587.
Therefore, the probability \( P(X < 8) \) for a normal distribution with a mean of 10 and a standard deviation of 2 is approximately 0.1587.
