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) In a study of TV viewing habits, it is desired to estimate the average number of hours that learners spend
watching per week. If it is reasonable to assume that
3.2
hours, how large a sample is needed so that it
will be possible to assert with 95% confidence that the sample mean is off by less than 20 minutes? �
A fair 6 sided die is rolled twice, determine the probability of obtaining the sum of the numbers less than 5.
Given a die it has 6 faces in which gas either dot of x = 1, 2,3, 4, 5,6. Consider the sample of size n= 3. Illustrate the sampling distrubution and the central limit theorem.
Q2. A school organized a book fair and in this book fair a book seller is selling his books under the following rules:
There are three different packages available.
First package contains 2 Islamic books, 2 Science books and 2 Geography books, second package contains 2 Islamic books, 4 Science books and 1 Geography books and third package contains 3 Islamic books, 4 Science books and 5 Geography books. The book fair has a total of 250 Islamic books, 300 Science books, and 270 Geography books. First package makes a profit of Rs. 120, second package makes Rs.100 and third package makes Rs.270 per pack.
How many packs should be made to maximize book fair profits?
What will the profit be?
A string of iength L is stretched and fastened to two fix points. Find the solution of
the r.{ave equatiorl (vibrating string) ytt = a^2.yxx, when initial displacernent
y(x,0) = f (x) = b sin (pi.x / t).
also find the Fourier cosine transformation of exp(-x^2)
find the minimal polynomial of the linear operator t : R³ "- R³" define by t (x,y,z) =(x+2y+3z, 4y+5z,6 z).is t
10. A can of cat food, guaranteed by the manufacturer to contain at least 10 units of protein, 20 units of mineral matter, and 6 units of fat, consists of a mixture of four different ingredients. Ingredient A contains 10 units of protein, 2 units of mineral matter, and 1 2 unit of fat per 100g. Ingredient B contains 1 unit of protein, 40 units of mineral matter, and 3 units of fat per 100g. Ingredient C contains 1 unit of protein, 1 unit of mineral matter, and 6 units of fat per 100g. Ingredient D contains 5 units of protein, 10 units of mineral matter, and 3 units of fat per 100g. The cost of each ingredient is Birr 3, Birr 2, Birr 1, and Birr 4 per 100g, respectively. How many grams of each should be used to minimize the cost of the cat food, while still meeting the guaranteed composition? (Hint: Solve through simplex model)
Determine the volume of the solid/ring obtained by the region bounded by
𝑦=2√𝑥−1and 𝑦=𝑥−1 about line x= -1 using shell method
Given the following 2 premises, 1. 𝑝 → (𝑞 ∨ 𝑟) 2. 𝑞 → 𝑠 Prove 𝑝 → (𝑟 ∨ 𝑠) is valid using the Proof by Contradiction method.
A jar contains 8 green, 4 blue, 10 red and 2 yellow skittles A skittle is randomly drawn Replaced then another is drawn Find each probability blue
