Which angles are supplementary to angle BFE?
1 answer:
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A) 0.1587
B) 0.9772
C) 0.8185
Step-by-step explanation:
A)
In this problem, the mathematics score of the year is distributed according to a normal distribution, with parameters:
is the mean of the distribution
is the standard deviation of the distribution
We want to find the probability that a randomly selected score is greater than 30.4. First of all, we calculated the z-score associated to this value, which is given by:
The z-score tables give the probability that the z-score is less than a certain value; since the distribution is symmetrical around 0,
Here we want to find , which is therefore equivalent to
. Looking at the z-tables, we find that
B)
Here instead we want to find the probability that a randomly selected score is less than 32.8.
First of all, we calculate again the z-score associated to this value:
Now we notice that:
(1)
Since the overall probability under the curve must be 1. We also note that (from part A)
Which means that we can rewrite (1) as
Here, we have
Z = 2
This means that
Looking at the z-tables, we find that
Therefore, we get
C)
Here we want to find the probablity that the score is between 25.6 and 32.8.
First of all, we calculate the z-scores associated to these two values:
So here we basically want to find the probability that
Which can be rewritten as:
So in this case,
From part A and B we found that:
Therefore,