Tests scores for a statistics class have a mean of 82 and standard deviation of 2. A histogram shows a non-normal distribution. What is the value for k for the interval between 74 and 90 scores?

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.

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