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:
I attached a screenshot with the complete question.
Answer:x-coordinate of point w is nearly -3.5
Explanation:To get the x-coordinate of a certain point, we would need to read the value of this point on the horizontal axis (the x-axis).
Taking a look at point w, we would find that it is in the second quadrant. This means that it has a negative x-value.
Now, reading the x-value on the horizontal axis, we can see that it is nearly midway between points -3 and -4.
This means that point w is approximately -3.5
Hope this helps :)
He bought 3 scoops, each costing $1.19
The cost of the three scoops= 3*1.19= $3.57
Total cost of scoops and toppings is $4.55
Cost of toppings only= 4.55-3.57= $0.98
Each topping costs $0.49
Therefore number of toppings bought= 0.98/0.49= 2
Answer: 2 toppings
Answer:
1. 3x + 2
2. 0.25x - 6.5
3. $5.50 per sandwich
Step-by-step explanation:
1.
6x + 1 - (3x - 1)
PEMDAS says solve everything in the parentheses first
There is nothing left to simplify within the parentheses.
Since there's also no exponents, multiplication, or division, let's combine like terms starting from left to right
6x - 3x + 1 + 1
Negative + Negative = Positive, hence why it became 1 + 1
3x + 2
2.
(3x - 1) - 2.75 (x + 2)
PEMDAS says to do multiplication next (since parentheses are fully simplified and there are no exponents)
(3x - 1) - 2.75x - 5.5
Negative + Positive = Negative, hence why it became -5.5
3x - 1 - 2.75x - 5.5
Combine like terms
3x - 2.75x - 1 - 5.5
0.25x - 6.5
3.
Set up an equation:
Variable x = cost of sandwiches
4x + 4(2) = 30
4x + 8 = 30
Subtract 8 from both sides to isolate the variable
4x + 8 - 8 = 30 - 8
4x = 22
Divide both sides by 4
4x ÷ 4 = 22 ÷ 4
x = 5.5
$5.50 per sandwich
What do you mean instead it is true 4x6 is 24 but if you 1/4 x 6 is 6/4 or 1 1/2
