Question

What is the maximum number of standard deviations within which at least 98.44% of the data in any data set lies?

a) 1.5
b) 2
c) 2.5
d) 3

Answer 1

The maximum number of standard deviations within which at least 98.44% of the data in any data set lies is 2.5 standard deviations, which is option c).

Step-by-step explanation:

The question asks about the maximum number of standard deviations within which at least 98.44% of the data in any data set lies. According to the Empirical Rule, which applies to bell-shaped, symmetric distributions:

• About 68% of the data lies within one standard deviation of the mean.
• Approximately 95% of the data lies within two standard deviations of the mean.
• More than 99% of the data lies within three standard deviations of the mean.

Given that at least 98.44% of the data should lie within the specified number of standard deviations, the correct answer to the question is:

c) 2.5 standard deviations

This is because 95% is covered by two standard deviations and over 99% by three standard deviations - 2.5 standard deviations would lie somewhere between these two percentages, thus covering at least 98.44% of the data.