Final answer:
In a normal distribution, about 0.3% of cases lie more than three standard deviations from the mean. For a distribution of 1,000 cases, this means approximately 3 cases will be farther than +3 standard deviations from the mean.
Step-by-step explanation:
The question is asking how many cases will be farther away from the mean than +3 standard deviations in a normal distribution.
In a normal distribution, approximately 99.7% of data lies within three standard deviations from the mean.
This leaves about 0.3% of data outside of this range. Since the question specifies a normal distribution of 1,000 cases, we calculate the number of cases beyond three standard deviations by finding 0.3% of 1,000.
To find this, we can use the calculation:
0.003 × 1,000 = 3 cases
Hence, there will be approximately 3 cases that lie more than three standard deviations away from the mean in either direction on the normal curve, considering both tails of the distribution.