Answer:
This interval is between 1.5 and 15.5.
Step-by-step explanation:
Tchebysheff's Theorem
The Tchebysheff's Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by .
In this question, we have that:
Mean = 8.5
Standard deviation = 3.5
The manager wants to publish an interval in which at least 75% of these values lie.
By the Tchebysheff's Theorem, at least 75% of the measures are within 2 standard deviations of the mean.
8.5 - 2*3.5 = 1.5
8.5 + 2*3.5 = 15.5
This interval is between 1.5 and 15.5.