Tammy is buying a soft toy from a shop. The cost of the toy is 9 dollars and she also has to pay a sales tax that is 15% of the
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Answer:
By putting x = -x in f(x) i.e. f(-x) we didn't get f(x) or -f(x) so, the function is neither even nor odd.
Step-by-step explanation:
We need to explain why the function of is neither even or odd
First we will understand, when the function is even and odd
Even function:
<em>A function is even if f(-x) = f(x) </em>
Odd function:
<em>A function is odd if f(-x) = -f(x) </em>
So, if we get the above result by putting x = -x, then we can say that the function is even or odd.
If we don't get any of the above results then the function is neither even nor odd.
So, for the given function:
Put x = -x
So, by putting x=-x in f(x) i.e. f(-x) we didn't get f(x) or -f(x) so, the function is neither even nor odd.
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].