Respuesta :
Answer:
k=4
Step-by-step explanation:
The empirical rule is only applicable on normal distribution while Chebyshev’s theorem is applicable to all type of distribution.
Chebyshev’s theorem states that at least 1-1/k² of data lies within μ±kσ interval.
We have to find the value of k for interval (74,90).
We are given that mean=μ=82 and standard deviation=σ=2
μ-kσ=74
82-k*2=74
82-74=2k
8/2=k
k=4.
Or
μ+kσ=90
82+k*2=90
2k=90-82
2k=8
k=8/2
k=4.
Thus, for k=4 for the interval between 74 and 90 scores.
So, the required value is [tex]k=4[/tex]
Standard deviation:
The standard deviation formula is used to find the values of a particular data that is dispersed.
It is given that,
[tex]\mu=82\\\sigma=2[/tex]
Then,
[tex]k=\frac{x-mean}{\sigma} \\k=\frac{90-82}{2} \\k=4[/tex]
Learn more about the topic standard deviation:
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