Can someone please help me with math.
2 answers:
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Answer:
(a) P (<em>Z</em> < 2.36) = 0.9909 (b) P (<em>Z</em> > 2.36) = 0.0091
(c) P (<em>Z</em> < -1.22) = 0.1112 (d) P (1.13 < <em>Z</em> > 3.35) = 0.1288
(e) P (-0.77< <em>Z</em> > -0.55) = 0.0705 (f) P (<em>Z</em> > 3) = 0.0014
(g) P (<em>Z</em> > -3.28) = 0.9995 (h) P (<em>Z</em> < 4.98) = 0.9999.
Step-by-step explanation:
Let us consider a random variable, , then
, is a standard normal variate with mean, E (<em>Z</em>) = 0 and Var (<em>Z</em>) = 1. That is,
.
In statistics, a standardized score is the number of standard deviations an observation or data point is above the mean. The <em>z</em>-scores are standardized scores.
The distribution of these <em>z</em>-scores is known as the standard normal distribution.
(a)
Compute the value of P (<em>Z</em> < 2.36) as follows:
P (<em>Z</em> < 2.36) = 0.99086
≈ 0.9909
Thus, the value of P (<em>Z</em> < 2.36) is 0.9909.
(b)
Compute the value of P (<em>Z</em> > 2.36) as follows:
P (<em>Z</em> > 2.36) = 1 - P (<em>Z</em> < 2.36)
= 1 - 0.99086
= 0.00914
≈ 0.0091
Thus, the value of P (<em>Z</em> > 2.36) is 0.0091.
(c)
Compute the value of P (<em>Z</em> < -1.22) as follows:
P (<em>Z</em> < -1.22) = 0.11123
≈ 0.1112
Thus, the value of P (<em>Z</em> < -1.22) is 0.1112.
(d)
Compute the value of P (1.13 < <em>Z</em> > 3.35) as follows:
P (1.13 < <em>Z</em> > 3.35) = P (<em>Z</em> < 3.35) - P (<em>Z</em> < 1.13)
= 0.99960 - 0.87076
= 0.12884
≈ 0.1288
Thus, the value of P (1.13 < <em>Z</em> > 3.35) is 0.1288.
(e)
Compute the value of P (-0.77< <em>Z</em> > -0.55) as follows:
P (-0.77< <em>Z</em> > -0.55) = P (<em>Z</em> < -0.55) - P (<em>Z</em> < -0.77)
= 0.29116 - 0.22065
= 0.07051
≈ 0.0705
Thus, the value of P (-0.77< <em>Z</em> > -0.55) is 0.0705.
(f)
Compute the value of P (<em>Z</em> > 3) as follows:
P (<em>Z</em> > 3) = 1 - P (<em>Z</em> < 3)
= 1 - 0.99865
= 0.00135
≈ 0.0014
Thus, the value of P (<em>Z</em> > 3) is 0.0014.
(g)
Compute the value of P (<em>Z</em> > -3.28) as follows:
P (<em>Z</em> > -3.28) = P (<em>Z</em> < 3.28)
= 0.99948
≈ 0.9995
Thus, the value of P (<em>Z</em> > -3.28) is 0.9995.
(h)
Compute the value of P (<em>Z</em> < 4.98) as follows:
P (<em>Z</em> < 4.98) = 0.99999
≈ 0.9999
Thus, the value of P (<em>Z</em> < 4.98) is 0.9999.
**Use the <em>z</em>-table for the probabilities.
I am somehow confused with the given matrix. Because usually, when the system of equations is given as:
ax + by = c
dx + ey = f
the matrix would be written in this manner:
![\left[\begin{array}{ccc}a&b&c\\d&e&f\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%26c%5C%5Cd%26e%26f%5Cend%7Barray%7D%5Cright%5D%20)
Let me just assume that the arrangement of the given corresponds to this system of equations:
4x + 8y = 0
2x + 5y = 6
So you write it as
![\left[\begin{array}{ccc}4&8&0\\2&5&6\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%268%260%5C%5C2%265%266%5Cend%7Barray%7D%5Cright%5D%20)
In order to solve this, the matrix should look like this where x and y are the answers
![\left[\begin{array}{ccc}1&0&x\\0&1&y\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26x%5C%5C0%261%26y%5Cend%7Barray%7D%5Cright%5D%20)
So, the first thing to do is apply this pattern: Row 2 = Row 1 - 2*Row 2. The result will be
![\left[\begin{array}{ccc}4&8&0\\0&-2&-12\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%268%260%5C%5C0%26-2%26-12%5Cend%7Barray%7D%5Cright%5D%20)
Next, Row 1 = (Row 1/4) + R2:
![\left[\begin{array}{ccc}1&0&-12\\0&-2&-12\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-12%5C%5C0%26-2%26-12%5Cend%7Barray%7D%5Cright%5D%20)
Lastly, Row 2 = Row 2 / -2:
![\left[\begin{array}{ccc}1&0&-12\\0&1&6\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-12%5C%5C0%261%266%5Cend%7Barray%7D%5Cright%5D%20)
Thus, the answer is x=-12 and y=6.
ax + by = c
dx + ey = f
the matrix would be written in this manner:
Let me just assume that the arrangement of the given corresponds to this system of equations:
4x + 8y = 0
2x + 5y = 6
So you write it as
In order to solve this, the matrix should look like this where x and y are the answers
So, the first thing to do is apply this pattern: Row 2 = Row 1 - 2*Row 2. The result will be
Next, Row 1 = (Row 1/4) + R2:
Lastly, Row 2 = Row 2 / -2:
Thus, the answer is x=-12 and y=6.
Answer:
Not proportional.
Step-by-step explanation:
A proportional relationship is a relationship which crosses through the origin (0,0) and which has a proportional constant. We can determine this either by finding (0,0) where x=0 and y=0 in the table or by dividing y/x. None of the tables contain (0,0) so we will divide y by x. We are looking for a table which when each y is divided by its x we have the same constant appearing.
Though it has a point at the origin, these fractions are not equal. This is not proportional.