Step 1 :First, we need to standardize the interval. The standardization formula is \(Z = \frac{X - \mu}{\sigma}\), where \(X\) is the value from the original distribution, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
Step 2 :For the lower limit of the interval, -60, the standardized value is \(Z = \frac{-60 - (-30)}{30} = -1\).
Step 3 :For the upper limit of the interval, -30, the standardized value is \(Z = \frac{-30 - (-30)}{30} = 0\).
Step 4 :Now, we need to find the area under the standard normal curve between -1 and 0. This is equivalent to finding the probability that a standard normal random variable falls in this interval.
Step 5 :From the standard normal distribution table, we find that the area to the left of 0 is 0.5000 and the area to the left of -1 is 0.1587.
Step 6 :Subtracting these two areas gives the area between -1 and 0, which is \(0.5000 - 0.1587 = 0.3413\).
Step 7 :So, the area under the normal curve and above the interval [-60, -30] on the horizontal axis is \(\boxed{0.3413}\).