Respuesta :
Answer:
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 [tex](\bar{x}-ks,\bar{x}+ks)[/tex]) is at least [tex]1-\frac{1}{k^2}[/tex], where k > 1.
Given:
[tex]\bar{x}=30\\s=5[/tex]
The interval (15, 45) is the one that is formed by adding and subtracting three standard deviations from the mean.
[tex](\bar{x}-ks,\bar{x}+ks)[/tex]
[tex](30-3\cdot 5,30+3\cdot 5)=(15,45)[/tex]
By Chebyshev’s Theorem, at least [tex]1-\frac{1}{3^2}=\frac{8}{9}[/tex] of the data are within this interval. Since [tex]\frac{8}{9}[/tex] 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).
