I know don't know if this right P(X)<115)= 12.1 (115-mean) how do I get the mean or is there 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?

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.121) and its Z score. Z score = -1.27 is standard deviations below the mean.

115 + 1.27(1.2) = mean

To find the mean value, you need to use the Z-score formula in conjunction with the standard normal distribution table.

Here's how you can solve this problem step by step:

1. Start with the given equation: P(X < 115) = 0.121.

2. Convert the original distribution into a standard normal distribution by using the Z-score formula: Z = (X - μ) / σ, where Z is the standard score, X is the observed value (115V in this case), μ is the mean of the distribution, and σ is the standard deviation.

3. Rearrange the formula to solve for the mean (μ): μ = X - Z * σ.

4. Look up the corresponding Z-score in the standard normal distribution table for the probability of 0.121. In this case, the Z-score is approximately -1.206.

5. Substitute the given values into the formula and solve for the mean:
μ = 115 - (-1.206) * 1.20.

6. Simplify the calculation:
μ = 115 + 1.4472.
μ ≈ 116.4472.

Therefore, the mean line voltage would have to be approximately 116.4472 volts in order for 12.1% of the line voltages to fall below 115V.