Final answer:
To find the mean monthly payment, use the z-score formula to determine the value of one-fourth of the payments above $1255.94. The mean monthly payment is $1235.94.
Step-by-step explanation:
To find the mean monthly payment, we need to determine the value of one-fourth of the payments above $1255.94. Since the distribution is normal, we can use the z-score formula to find the corresponding z-score. The z-score formula is given by: z = (x - mean) / standard deviation.
From the question, we know that one-fourth of the payments are above $1255.94. This means that the z-score corresponding to $1255.94 is 0.25. We can rearrange the z-score formula to solve for the mean:
mean = x - (z * standard deviation)
Substituting the values, we get:
mean = $1255.94 - (0.25 * $120)
mean = $1235.94
Therefore, the mean monthly payment is $1235.94.