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
9514 1404 393
Answer:
Step-by-step explanation:
The form of the equation you are given is called "point-slope" form. The "slope" in this case is the per-hour fee. The point is (9 h, $195). Point-slope form generally looks like this:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Here, you have m=15, (h, k) = (9, 195), so the equation looks like ...
y -195 = 15(x -9)
__
The "one-time fee" is the cost when hours are zero.
y -195 = 15(0 -9)
y = 195 -9(15) = 60 . . . . add 195 to both sides, and evaluate
The one-time fee is $60.
Using proportions, it is found that the same job will take Mrs. Squirrel 6 hours.
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The times are given as follows:
- Mr. Pigeon: 30 minutes = Half an hour = 1/48 day.
The ratios are as follows:
Turtle/Squirrel = Squirrel/Pigeon.
Hence:
x = 1/4.
It takes 1/4 of a day for Mrs. Squirrel to do the job, hence 1/4 x 24 hours = 6 hours.
More can be learned about proportions at brainly.com/question/24372153
#SPJ1
Answer:
8
Step-by-step explanation:
( 12 + 3m ) / 2 = 18
12 + 3m = 18 x 2
12 + 3m = 36
3m = 36 - 12
3m = 24
m = 24 / 3
m = 8
