Answer:
The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.
Step-by-step explanation:
The confidence interval for population variance is given as below:
![[(n - 1)\times S^{2} / X^{2} \alpha/2, n-1 ] < \alpha < [(n- 1)\times S^{2} / X^{2} 1- \alpha/2, n- 1 ]](https://tex.z-dn.net/?f=%5B%28n%20-%201%29%5Ctimes%20S%5E%7B2%7D%20%20%2F%20%20X%5E%7B2%7D%20%20%5Calpha%2F2%2C%20n-1%20%5D%20%3C%20%5Calpha%20%3C%20%5B%28n-%201%29%5Ctimes%20S%5E%7B2%7D%20%20%2F%20X%5E%7B2%7D%201-%20%5Calpha%2F2%2C%20n-%201%20%5D)
We are given
Confidence level = 98%
Sample size = n = 81
Degrees of freedom = n – 1 = 80
Sample Variance = S^2 = 3.23
![X^{2}_{[\alpha/2, n - 1]} = 112.3288\\\X^{2} _{1 -\alpha/2,n- 1} = 53.5401](https://tex.z-dn.net/?f=X%5E%7B2%7D_%7B%5B%5Calpha%2F2%2C%20n%20-%201%5D%7D%20%20%20%3D%20112.3288%5C%5C%5CX%5E%7B2%7D%20_%7B1%20-%5Calpha%2F2%2Cn-%201%7D%20%3D%2053.5401)
(By using chi-square table)
[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]
[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]
2.3004 < σ^2 < 4.8263
Lower limit = 2.30
Upper limit = 4.83.
Answer:
-1/18
Step-by-step explanation:
Answer:
10 classes
Step-by-step explanation:
Given equations in the question
Dance World: y = 15x
Toe Tappers: y = 25 + 12.5x
Where,
x = number of classes
Equate the total cost at both dance studios
15x = 25 + 12.5x
Collect like terms
15x - 12.5x = 25
2.5x = 25
Divide both sides by 2.5
2.5x / 2.5 = 25 / 2.5
x = 10 classes
x = number of classes = 10
Answer:
A total of 119 Specials were sold today. Chicken Littles had the highest number sold, which represents about 21% (25/119 * 100) of the total sales and a cost of 24% of the total costs. This was followed by Huge Burger and Coney Dog which were sold 20 each or about 17% of the number sold. Poker Burger, Baby Burger, and Yummy trailed behind with total sales of 19, 18, and 17 respectively.
Step-by-step explanation:
a) Data and Calculations:
SPECIAL NUMBER SOLD Percentage COST Percentage
Huge Burger 20 17% $2.95 20%
Baby Burger 18 15% $1.49 10%
Chicken Littles 25 21% $3.50 24%
Porker Burger 19 16% $2.95 20%
Yummy Burger 17 14% $1.99 13%
Coney Dog 20 17% $1.99 13%
Total Specials Sold 119 100% $14.87 100%
Answer:
Discount: $41.25
Sale price: $123.74
Step-by-step explanation:
Discount=(Original price)x((discount %)/(100))
164.99x(25/100)
164x0.25
=$41.25
Sale price= (original price) - (discount)
164.99 - 41.25
= $123.74
