How need help with this one. This is what I know

P(X)<115)= 12.1
(115-mean) how do I get the mean or is their a formula that can help me solve this?

A population of line voltages has a standard deviation of 1.20 volts. What value would the mean line voltage have to be so that 12.1% of the line voltages fell below 115V?

To find the mean line voltage for which 12.1% of the line voltages fall below 115V, you can use the properties of a standard normal distribution. Here's how you can approach this problem:

Step 1: Convert the given probability into a Z-score.
We know that the standard normal distribution has a mean of 0 and a standard deviation of 1. To find the Z-score, which represents the number of standard deviations away from the mean, we can use the formula:

Z = (X - mean) / standard deviation

In this case, we are given P(X < 115) = 0.121, so we want to find the Z-score for this probability.

Step 2: Find the Z-score from a standard normal distribution table.
To find the Z-score corresponding to a probability of 0.121, you can refer to a standard normal distribution table or use a statistical calculator. Looking up the closest value to 0.121, we find that the Z-score is approximately -1.18.

Step 3: Solve for the mean using the Z-score.
Now that we have the Z-score, we can rearrange the formula for Z to solve for the mean:

Z = (X - mean) / standard deviation

Rearranging the formula gives us:

mean = X - (Z * standard deviation)

Substituting in the known values:

mean = 115 - (-1.18 * 1.20)

Calculating this expression gives us the mean line voltage:

mean ≈ 116.416

So, the mean line voltage would need to be approximately 116.416 volts in order for 12.1% of the line voltages to fall below 115V.