A quantitative data set of size 80 has mean 30 and standard deviation 5. At least how many observations lie between 15 and 45?

At least 71 observations must lie inside the interval (15, 45).

Step-by-step explanation:

According with the Chebyshev’s Theorem, for any data set, the proportion (or percentage) of values that fall within k standard deviations from mean (that is, in the interval ) is at least , where k > 1.

Given:

The interval (15, 45) is the one that is formed by adding and subtracting three standard deviations from the mean.

By Chebyshev’s Theorem, at least of the data are within this interval. Since of 80 is 71.11, this means that at least 71.11 observations are in the interval. But one cannot take a fractional observation, so we conclude that at least 71 observations must lie inside the interval (15, 45).

step-by-step explanation: