Carol has a choice of an account that compounds quarterly and an account that compounds daily.
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Answer:
The linear function becomes:
y = 15x + 10
Here, 'x' is the number of hours, b=10 is the initial service fee i.e. $10, 15 is slope or rate of change, and 'y' is the cost.
Step-by-step explanation:
We know that the slope-intercept of a linear function is
where m is the slope and b is the y-intercept
Note: Slope is also termed as the 'rate of change'.
Given that Aron charges an initial service fee of 10$.
Thus, the y-intercept = b = 10
As the rate of change = 15$ per hour
so the slope = m = 15
Therefore, the linear function becomes:
y = 15x + 10
Here, 'x' is the number of hours, b=10 is the initial service fee i.e. $10, 15 is slope or rate of change, and 'y' is the cost.
For example, in one hour i.e. x = 1, the cost 'y' will be:
y = 15x + 10
y = 15(1) + 10
y = 25 + 10
y = $25
Therefore, in one hour (x=1), the cost will be: y = $25
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.