Complex roots problem
1 answer:
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First notice that the triangle with sides 
and the triangle with sides 
are similar. This is true because the angle between sides 
in the smaller triangle is clearly 
, while the angle between sides 
in the larger triangle is clearly 
. So the triangles are similar with sides corresponding to 
, respectively.
Now both triangles are
, which means there's a convenient ratio between its sides. If the length of the shortest leg is 
, then the length of the longer leg is 
and the hypotenuse has length 
.
Since
is the shortest leg in the larger triangle, it follows that 
, so 
Now both triangles are
Since
Answer:
At least 202.44 mm in the top 15%.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
How many yearly mm of rainfall would there be in the top 15%?
At least X mm.
X is the 100-15 = 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037.
At least 202.44 mm in the top 15%.