We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:
The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:
![CI(\mu)=\lbrack x-Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}},x+Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}}\rbrack](https://tex.z-dn.net/?f=CI%28%5Cmu%29%3D%5Clbrack%20x-Z_%7B1-%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Ccdot%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%5B%5D%7Bn%7D%7D%2Cx%2BZ_%7B1-%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Ccdot%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%5B%5D%7Bn%7D%7D%5Crbrack)
Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:
![CI(\mu)=\lbrack30.0-Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}},30.0+Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}}\rbrack](https://tex.z-dn.net/?f=CI%28%5Cmu%29%3D%5Clbrack30.0-Z_%7B0.99%7D%5Ccdot%5Cfrac%7B2.40%7D%7B%5Csqrt%5B%5D%7B28%7D%7D%2C30.0%2BZ_%7B0.99%7D%5Ccdot%5Cfrac%7B2.40%7D%7B%5Csqrt%5B%5D%7B28%7D%7D%5Crbrack)
Where (from tables):
Finally, the interval at 98% confidence level is:
Answer:
3: 2q − 4 = 20
Step-by-step explanation:
Solve for q:
2 q - 4 = 20
Add 4 to both sides:
2 q + (4 - 4) = 4 + 20
4 - 4 = 0:
2 q = 20 + 4
20 + 4 = 24:
2 q = 24
Divide both sides of 2 q = 24 by 2:
(2 q)/2 = 24/2
2/2 = 1:
q = 24/2
The gcd of 24 and 2 is 2, so 24/2 = (2×12)/(2×1) = 2/2×12 = 12:
Answer: q = 12
Assuming you're just computing the volume, i.e.
we should convert to cylindrical coordinates first, setting
so that the volume is given by
which has a value of
.
Answer:
144
Step-by-step explanation:
your welcome
Let’s start off by subtracting 5 from 10 leaving 5 dollars
if 6 tickets cost 3 dollars she can only buy 6 tickets because she will only have 2 dollars left
