Answer: rental is $415, and the standard deviation is $5.
Explanation:
If about 99.7 percent of the monthly rentals fall between 400 and 430, it implies that this range encompasses three standard deviations from the mean.
To calculate the mean, we can find the midpoint of the given range:
Mean = (400 + 430) / 2 = 415
Since the range of three standard deviations covers about 99.7 percent of the data in a normal distribution, we can use this information to estimate the standard deviation (σ).
Standard deviation (σ) = (430 - 415) / 3 = 15 / 3 = 5
Therefore, based on the given information, the mean monthly rental is $415, and the standard deviation is $5.