101k views
3 votes
If the mean of a given dataset is 600,000 and the standard deviation is 19,000, where is a majority of the data expected to lie based on the empirical rule for a normal distribution?

User Samira
by
7.8k points

1 Answer

3 votes

Final answer:

The majority of the data in the given dataset is expected to lie between 562,000 and 638,000 based on the empirical rule.

Step-by-step explanation:

The empirical rule states that for a bell-shaped and symmetric distribution, approximately 68 percent of the data will fall within one standard deviation of the mean, approximately 95 percent will fall within two standard deviations, and more than 99 percent will fall within three standard deviations. In the given dataset with a mean of 600,000 and a standard deviation of 19,000, we can apply the empirical rule to determine where the majority of the data is expected to lie.

One standard deviation above and below the mean: 600,000 ± 19,000 = 581,000 to 619,000

Two standard deviations above and below the mean: 600,000 ± (2 × 19,000) = 562,000 to 638,000

Three standard deviations above and below the mean: 600,000 ± (3 × 19,000) = 543,000 to 657,000

Therefore, the majority of the data in the given dataset is expected to lie between 562,000 and 638,000 based on the empirical rule.

User Harun ERGUL
by
8.2k points