Answer:
Answer and Explanation:
We have:
Population mean,
μ
=
3
,
000
hours
Population standard deviation,
σ
=
696
hours
Sample size,
n
=
36
1) The standard deviation for the sampling distribution:
σ
¯
x
=
σ
√
n
=
696
√
36
=
116
2) By the central limit theorem, the sampling distribution's expected value matches the population mean.
Thus:
The expected value of the sampling distribution equals the population mean,
μ
¯
x
=
μ
=
3
,
000
The standard deviation of the sampling distribution,
σ
¯
x
=
116
The sampling distribution of
¯
x
is roughly normal due to a sample size greater than
30
.
3) The likelihood that the average lifespan of the sample falls between
2670.56
and
2809.76
hours:
P
(
2670.56
<
x
<
2809.76
)
=
P
(
2670.56
−
3000
116
<
z
<
2809.76
−
3000
116
)
=
P
(
−
2.84
<
z
<
−
1.64
)
=
P
(
z
<
−
1.64
)
−
P
(
z
<
−
2.84
)
=
0.0482
In Excel: =NORMSDIST(-1.64)-NORMSDIST(-2.84)
4) The probability of the average life in the sample exceeding
3219.24
hours:
P
(
x
>
3219.24
)
=
P
(
z
>
3219.24
−
3000
116
)
=
P
(
z
>
1.89
)
=
0.0294
In Excel: =NORMSDIST(-1.89)
5) The likelihood that the sample's average life is lower than
3180.96
hours:
P
(
x
<
3180.96
)
=
P
(
z
<
3180.96
−
3000
116
)
=
P
(
z
<
1.56
)
=
0.9406
Answer: x1 = 251/26, x2 = -111/26
Step-by-step explanation:
Greetings!
As illustrated in the diagram, the point you seek is where the two lines intersect.
This intersection point is found by solving the system of linear equations (both equations must be satisfied by the point):

You can approach solving it using the substitution method:

Then substitute x1 into equation 2 to resolve x2:

After which, utilize the x2 value to establish x1:

Which equivalent fraction corresponds to

? -

since

-

as

and

-
because
and 
-
since 
The answer is
-
because
and 
A fraction is deemed equivalent if it maintains the same value when expressed in simplest terms. The equivalent to
is found in the chosen option;
First, halve both the numerator and denominator by 2

Then reduce further
2/2 = 1 and 6/2 = 3; Thus;

Next, multiply both the numerator and denominator by 3

Therefore,
equals
.
Answer:
E. P(W | H)
Step-by-step explanation:
Meaning of each probability:
P(H): Likelihood of the game occurring at home
P(W): Likelihood of the game resulting in a win.
P(H and W): Likelihood that the game is both at home and a win.
P(H|W): Likelihood of a win occurring when at home.
P(W|H): Likelihood of winning at home games.
Which probabilities are necessary to determine the fraction of home games that were victories?
This is the probability of winning a home game. Hence, the answer is:
E. P(W | H)