To solve for the confidence interval for the true average
percentage elongation, we use the z statistic. The formula for confidence
interval is given as:
Confidence interval = x ± z σ / sqrt (n)
where,
x = the sample mean = 8.63
σ = sample standard deviation = 0.79
n = number of samples = 56
From the standard distribution tables, the value of z at
95% confidence interval is:
z = 1.96
Therefore substituting the known values into the
equation:
Confidence interval = 8.63 ± (1.96) (0.79) / sqrt (56)
Confidence interval = 8.63 ± 0.207
Confidence interval = 8.42, 8.84
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Answer:
(a) 3.75
(b) 2.00083
(c) 0.4898
Step-by-step explanation:
It is provided that X has a continuous uniform distribution over the interval [1.3, 6.2].
(a)
Compute the mean of X as follows:
(b)
Compute the variance of X as follows:
(c)
Compute the value of P(X < 3.7) as follows:
![P(X < 3.7)=\int\limits^{3.7}_{1.3}{\frac{1}{6.2-1.3}}\, dx\\\\=\frac{1}{4.9}\times [x]^{3.7}_{1.3}\\\\=\frac{3.7-1.3}{4.9}\\\\\approx 0.4898](https://tex.z-dn.net/?f=P%28X%20%3C%203.7%29%3D%5Cint%5Climits%5E%7B3.7%7D_%7B1.3%7D%7B%5Cfrac%7B1%7D%7B6.2-1.3%7D%7D%5C%2C%20dx%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B4.9%7D%5Ctimes%20%5Bx%5D%5E%7B3.7%7D_%7B1.3%7D%5C%5C%5C%5C%3D%5Cfrac%7B3.7-1.3%7D%7B4.9%7D%5C%5C%5C%5C%5Capprox%200.4898)
Thus, the value of P(X < 3.7) is 0.4898.
Solution:
A coin is flipped three times,resulting three heads in a row.
Since Steve has mentioned that , each flip of a coin is unconnected to the previous flip.
Two or more events are said to be independent if occurrence of one of them is not affected by the Occurrence of other.
This is an example of independent events.
In terms of probability, P (A∩B∩C)= P(A)×P(B)×P(C)
Answer:
And?
Step-by-step explanation:
