The 8th grade is selling tickets to the 8th grade formal.The cost per ticket is $15.The decorations and food cost $600,and each
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The fundamental theorem of algebra states that a polynomial with degree n has at most n solutions. The "at most" depends on the fact that the solutions might not all be real number.
In fact, if you use complex number, then a polynomial with degree n has exactly n roots.
So, in particular, a third-degree polynomial can have at most 3 roots.
In fact, in general, if the polynomial has solutions
, then you can factor it as
So, a third-degree polynomial can't have 4 (or more) solutions, because otherwise you could write it as
But this is a fourth-degree polynomial.
A suitable probability calculator can tell you the probability is about 6.7%.
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The standard deviation of the distribution of sample means is the population standard deviation (6) divided by the square root of the sample size (√144=12). Thus, your threshold is about (19.25-20)/(6/12) = -1.5 standard deviations from the mean.
