If m ∠ A B F = ( 7 b − 24 ) ° and m ∠ A B E = 2 b ° , find m ∠ E B F .
1 answer:
Based on the given parameters, the measure of m∠EBF is 5b − 24
<h3>How to determine the measure of EBF?</h3>The given parameters are:
m∠ABF = (7b − 24)°
m∠ABE = 2b°
See attachment for the illustrating diagram
From the diagram, we have the following equation
m∠EBF = m∠ABF - m∠ABE
Substitute the known values in the above equation
m∠EBF = (7b − 24)° - 2b°
Remove the bracket in the above equation
m∠EBF = 7b − 24 - 2b
Collect the like terms in the above equation
m∠EBF = 7b - 2b − 24
Evaluate the like terms in the above equation
m∠EBF = 5b − 24
Based on the given parameters, the measure of m∠EBF is 5b − 24
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Given Information:
Number of lithium batteries = n = 16
Mean life of lithium batteries = μ = 645 hours
Standard deviation of lithium batteries = σ = 31 hours
Confidence level = 95%
Required Information:
Confidence Interval = ?
Answer:
Step-by-step explanation:
The confidence interval is given by
Where μ is the mean life of lithium batteries, σ is the standard deviation, n is number of lithium batteries selected, and t is the critical value from the t-table with significance level of
tα/2 = (1 - 0.95) = 0.05/2 = 0.025
and the degree of freedom is
DoF = n - 1 = 16 - 1 = 15
The critical value (tα/2) at 15 DoF is equal to 2.131 (from the t-table)
Therefore, the 95% confidence interval is 628.5 to 661.5 hours
What does it mean?
It means that we are 95% confident that the mean life of 16 lithium batteries is within the interval of (628.5 to 661.5 hours)
Answer:
The margin of error of u is of 3.8.
The 99% confidence interval for the population mean u is between 27.4 minutes and 35 minutes.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 28 - 1 = 27
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 27 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.7707
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The margin of error of u is of 3.8.
The lower end of the interval is the sample mean subtracted by M. So it is 31.2 - 3.8 = 27.4 minutes
The upper end of the interval is the sample mean added to M. So it is 31.2 + 3.8 = 35 minutes
The 99% confidence interval for the population mean u is between 27.4 minutes and 35 minutes.