What is the average of two opposite numbers?
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The table when completed looks like this:
x -2 -1 0 1 2
f(x) 4 2 1 2 4.
We plot these points on the graph: (-2, 4), (-1, 2), (0, 1), (1, 2), (2, 4).
<h3>What is a function?</h3>A function exists as a relation between a dependent variable (f(x)) and an expression of an independent variable (x), utilized to define the value of a dependent variable from a provided value of an independent variable.
We have been given a function,
We have to estimate the value of f(x) when x = {-2, -1, 0, 1, 2}
If the values of x ≤ 0, take f(x) = (1/2)ˣ then
f(-2) = (1/2)⁻² = 2² = 4
f(-1) = (1/2)⁻¹ = 2¹ = 2
f(0) = (1/2)⁰ = 1
If the values of x > 0, take f(x) = 2ˣ then
f(1) = 2¹ = 2
f(2) = 2² = 4
The table exists as follows
x -2 -1 0 1 2
f(x) 4 2 1 2 4.
We plot these points on the graph: (-2, 4), (-1, 2), (0, 1), (1, 2), (2, 4).
To learn more about independent and dependent variable refer to:
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We are given the following data:
Average = m = 123.6
Population standard deviation = σ= psd = 36.8
Sample Size = n = 22
We are to find the confidence intervals for 90%, 95% and 98% confidence level.
Since the population standard deviation is known, and sample size is not too small, we can use standard normal distribution to find the confidence intervals.
Part 1) 90% Confidence Interval
z value for 90% confidence interval = 1.645
Lower end of confidence interval =
Using the values, we get:
Lower end of confidence interval=
Upper end of confidence interval =
Using the values, we get:
Upper end of confidence interval=
Thus the 90% confidence interval will be (110.69, 136.51)
Part 2) 95% Confidence Interval
z value for 95% confidence interval = 1.96
Lower end of confidence interval =
Using the values, we get:
Lower end of confidence interval=
Upper end of confidence interval =
Using the values, we get:
Upper end of confidence interval=
Thus the 95% confidence interval will be (108.22, 138.98)
Part 3) 98% Confidence Interval
z value for 98% confidence interval = 2.327
Lower end of confidence interval =
Using the values, we get:
Lower end of confidence interval=
Upper end of confidence interval =
Using the values, we get:
Upper end of confidence interval=
Thus the 98% confidence interval will be (105.34, 141.86)
Part 4) Comparison of Confidence Intervals
The 90% confidence interval is: (110.69, 136.51)
The 95% confidence interval is: (108.22, 138.98)
The 98% confidence interval is: (105.34, 141.86)
As the level of confidence is increasing, the width of confidence interval is also increasing. So we can conclude that increasing the confidence level increases the width of confidence intervals.
Average = m = 123.6
Population standard deviation = σ= psd = 36.8
Sample Size = n = 22
We are to find the confidence intervals for 90%, 95% and 98% confidence level.
Since the population standard deviation is known, and sample size is not too small, we can use standard normal distribution to find the confidence intervals.
Part 1) 90% Confidence Interval
z value for 90% confidence interval = 1.645
Lower end of confidence interval =
Using the values, we get:
Lower end of confidence interval=
Upper end of confidence interval =
Using the values, we get:
Upper end of confidence interval=
Thus the 90% confidence interval will be (110.69, 136.51)
Part 2) 95% Confidence Interval
z value for 95% confidence interval = 1.96
Lower end of confidence interval =
Using the values, we get:
Lower end of confidence interval=
Upper end of confidence interval =
Using the values, we get:
Upper end of confidence interval=
Thus the 95% confidence interval will be (108.22, 138.98)
Part 3) 98% Confidence Interval
z value for 98% confidence interval = 2.327
Lower end of confidence interval =
Using the values, we get:
Lower end of confidence interval=
Upper end of confidence interval =
Using the values, we get:
Upper end of confidence interval=
Thus the 98% confidence interval will be (105.34, 141.86)
Part 4) Comparison of Confidence Intervals
The 90% confidence interval is: (110.69, 136.51)
The 95% confidence interval is: (108.22, 138.98)
The 98% confidence interval is: (105.34, 141.86)
As the level of confidence is increasing, the width of confidence interval is also increasing. So we can conclude that increasing the confidence level increases the width of confidence intervals.