you have a bag of marbles. 5 marbles are blue, 4 marbles are red, and 2 marbles are yellow. What is the probability that you pul
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Answer:
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 158.9
Standard Deviation, σ = 90.4
We are given that the distribution is a normal distribution.
Formula:
We have to find the value of x such that the probability is 0.39
Calculation the value from standard normal z table, we have,
133.68 separates the bottom 39% means from the top 61% means.
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].