Answer: (29.4, 32.6)
Step-by-step explanation:
From the question, we know that
Sample size (n) = 27
Sample mean (x) = $31
Sample standard deviation (s) = $3
We are to construct a 99% confidence interval interval for average amount spent on gift.
The formulae for constructing a 99% confidence interval for population mean is given as
u = x + tα/2 × s/√n...... For upper limit
u = x - tα/2 × s/√n...... For lower limit
tα/2 is the critical value for a 2 tailed test. This value of gotten from a t distribution table by checking the degree of freedom ( 27 - 1 = 26) against the level of significance ( 100% - 99% = 1%).
Hence tα/2 = 2.779
Let us substitute our parameters and solve
For lower limit
u = 31 - 2.779 × 3/√27
u = 31 - 2.779 ( 0.5773)
u = 31 - 1.6045
u = 29.4
For upper limit
u = 31 + 2.779 × 3/√27
u = 31 + 2.779 ( 0.5773)
u = 31 + 1.6045
u = 32.6
Hence the 99% confidence interval for population mean is given as 29.4, 32.6
Answer:
In order to solve this equation, you have to isolate the x and set it equal to a number. I chose to add 8x to both sides, making it -2x - 5 = 11. Then add 5 to both sides, making it -2x = 16. Divide both sides by -2 to get x = -8. -8 is your answer. Hope this helps!
Answer:
105 is your answer
Step-by-step explanation:
Let the two consecutive integers be: x , x + 1
Set the equation
x + x + 1 = 209
Simplify. Combine like terms.
(x + x) + 1 = 209
2x + 1 = 209
Isolate the x. Note the equal sign, what you do to one side, you do to the other.
Subtract 1 from both sides
2x + 1 (-1) = 209 (-1)
2x = 209 - 1
2x = 208
Isolate the x. Divide 2 from both sides
(2x)/2 = (208)/2
x = 208/2
x = 104
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Plug in 104 for x.
(x + 1) = (104) + 1 = 105
105 is your answer
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