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
Response:
Explanatory steps:
I am unsure as well. However, I can state that the first one is
Sarah is 40 years old and her mother is 64 years old.
d Step-by-step explanation: when f(x)=5......It can also be expressed as f(x)=1/125(625x). This is applicable to any whole number over one, with 1(625x)=625x. Therefore, since 125(1)=125, we find (625/125)x=5x.
The graphics that are missing can be found in the attachment.
Answer: Graphic of alternative D.
Step-by-step explanation: An inverse function is one that reverses another function: Typically, x denotes the variable while y is the function. In the case of an inverse function, y takes on the variable role and x becomes the function. For example, f(x) = y if and only if g(y) = x.
The graphic depicting an inverse function represents the reflection of the original function across the identity line y=x.
In each alternative provided in the image, the graphs illustrate a function paired with its inverse, however, in alternative D, the dashed line accurately represents the identity line y = x and its correlation with the function and its inverse. Therefore, Graph D is the valid option.
