Mr. James has cylindrical beakers that measure 4 inches in diameter and 9 inches high. What is the volume contained within the b
1 answer:
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9514 1404 393
Answer:
-3, 7, 8
Step-by-step explanation:
You can fill in the boxes from the table values as shown in the attachment.
The leading coefficient is negative because the parabola opens downward. The value of it is the change in y-value as x changes by 1 unit either side of the vertex.
The vertex is identified by the fact that the y-values are symmetrical either side of the vertex.
Answer:
(a) 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].
(b) 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].
Step-by-step explanation:
We are given that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.75.
(a) Also, the average porosity for 20 specimens from the seam was 4.85.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample average porosity = 4.85
= population standard deviation = 0.75
n = sample of specimens = 20
= true average porosity
<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>
<u>So, 95% confidence interval for the true mean, </u><u> is ;</u>
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u>95% confidence interval for</u> = [
,
]
= [ ,
]
= [4.52 , 5.18]
Therefore, 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].
(b) Now, there is another seam based on 16 specimens with a sample average porosity of 4.56.
The pivotal quantity for 98% confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample average porosity = 4.56
= population standard deviation = 0.75
n = sample of specimens = 16
= true average porosity
<em>Here for constructing 98% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>
<u>So, 98% confidence interval for the true mean, </u><u> is ;</u>
P(-2.3263 < N(0,1) < 2.3263) = 0.98 {As the critical value of z at 1% level
of significance are -2.3263 & 2.3263}
P(-2.3263 < < 2.3263) = 0.98
P( <
<
) = 0.98
P( <
<
) = 0.98
<u>98% confidence interval for</u> = [
,
]
= [ ,
]
= [4.12 , 4.99]
Therefore, 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].