Answer:
[ 66 ; 93 ] The interval for 95% of all winning scores of this season
Step-by-step explanation:
We will examine this question with the empirical rule. Empirical rule established, that for a standard normal distribution, of all values of a given population
μ + σ will contains 68.3 %
μ + 2σ will contains 95.5 % and
μ + 3σ will contains 99.7 %
We have to understand that the intervals for that mathematics expressions are:
μ ± 0.5σ or [ μ - 0.5*σ ; μ + 0.5*σ ]
μ ± 1σ or [ μ - σ ; μ + σ ]
μ ± 1.5σ [ μ - 1.5*σ ; μ + 1.5*σ ]
respectively.
Then the interval
[ μ - σ ; μ + σ ] will contains 95% of winning scores.
In this case
μ - σ = 79.5 - 13.5 = 66 and
μ + σ = 79.5 + 13.5 = 93
So our interval is
[ 66 ; 93 ]