a) Suppose that a random sample of size 80 has a sample mean of 1.69 ppb and a sample standard deviation of 0.25 ppb. Find a 95%
1 answer:
Answer: The confidence interval is 1.69ppb±0.055
Step-by-step explanation:
To find the confidence interval, first find the z* which is the appropriate z*-value related to the confidence interval of preference. As in this is 95%, z*-value = 1.96 (Note: The value is from the standard normal Z distribution).
With the z*-value, multiply by the division of the standard deviation and the square root of the sample size:
z*-value . σ/√n = 1.96 · = 0.055
The 95% confidence interval of the sample mean of 1.69 ppb is 1.69ppb±0.055ppb
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Answer:
a) The slope of the function is 3.
c) The equation is represented by .
d) The y-intercept of the function is 35.
Step-by-step explanation:
a) According to the statement, we must assume that number of pieces of mail that must be hand-sorted (dependent variable) is represented by a linear function in terms of time (independent variable). That is:
(1)
Where:
- Slope, measured in number of pieces per minute.
- Time, measured in minutes.
- Initial number of pieces of mail that must be hand-sorted (y-intercept), measured in pieces.
- Current number of pieces of mail that must be hand-sorted, measured in pieces.
From Geometry, we know that a line can be formed by know two distinct points. If we know that and
, then the following system of linear equations is formed:
(2)
(3)
The solution of the system of equations is:
and
The slope of the function is 3.
c) By (1) and using results from a) we conclude that the equation function is:
(4)
d) The y-intercept of the function is 35.