Select three names for the angle. B c a
1 answer:
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Answer:
Explained below.
Step-by-step explanation:
Denote the events as follows:
<em>C</em> = chess
<em>V</em> = volleyball
<em>B</em> = basketball
The data provided is as follows:
n (C) = 30
n (V) = 19
n (B) = 25
n (C ∩ V) = 14
n (B ∩ V) = 8
n (B ∩ C) = 15
n (C ∩ V ∩ B) = 5
Consider the Venn diagram below.
The number of students who played only chess is marked in pink:
n (Only C) = 6
The number of students who played only volleyball is marked in blue:
n (Only V) = 2
The number of students who played only basketball is marked in orange:
n (Only B) = 7
The number of students who played all three is marked in grey:
n (C ∩ V ∩ B) = 5
Answer:
The value for <em>k</em> is about k = 11.093kg.
Step-by-step explanation:
To answer this question, that is, P(x<k) = 0.85, we can use the standardized value for a raw score, or the formula for obtaining z-scores:
[1]
Where
is the raw score.
is the population mean.
is the population standard deviation.
In this case, we are asking to find a value x = k, so that 85% of the blocks have weights less than k (kg).
We have also to use the values for the <em>cumulative standard normal distribution</em> with and
to find the value of z that corresponds to a probability of 0.85.
First step: find the z that corresponds to the probability of 0.85.
To use the formula [1], as we previously mentioned, we first need to find the value of <em>z</em> that corresponds to a probability of 0.85 using the <em>cumulative standard normal distribution table</em> (available in any Statistics books or on the Internet). Then, for a cumulative probability of 0.85, the corresponding value for z = 1.03 (approximately).
Second step: solve the formula [1] for x.
Solving this formula for x, we have:
Then (without units):
So
Thus, this value for x = 11.093 equals the value for k (x = k) so that
Then
or
We can see the graph below showing this value of k = 11.093kg for which 85% of the blocks have weights less that it (x = k = 11.093kg).
