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A researcher of a cardboard manufacturing company would like to know the estimated thickness of the cardboard a machine produces How many cardboards should he measure if he wants to be 99% confident that the estimate is accurate to 1 mm. Study shows that the standard deviation is 3mm
The average time it takes a group of Senior High School students to complete a certain examination is 48.2 minutes. The standard deviation is 7 minutes. If 45 randomly selected college student take the examination, what is the probability that the mean time it takes the group to complete the test between 46 and 49 minutes?
Given a die, it has 6 faces in which each face has either dot/s of 𝑥=1,2,3,4,5 𝑎𝑛𝑑 6. Given it as the population, consider sample of size 𝑛=3. Find the population mean, population variance, population standard deviation, the mean, variance and standard deviation of the sampling distribution of the sample mean and illustrate its probability histogram of the sampling distribution of the sample means.
Consider a population consisting of 4, 7, 8, 13, 15 and 17. Suppose samples of size 3 are drawn from this population. Determine the total number of samples. *
QUESTION 4 Find the quadratic form q(X) that corresponds to the symmetric matrix
𝐴 = [ 1 2 3 2 − 1 2 3 2 − 1] ( is 3by3 matrix)
Let F be the R²-R function defined by f(x,y)=Inxy and let r be the R-R² function defined by r(t)=(e^t;t).
1.determine the composite function F o r: (simplify your answer).
2.determine gradf (x,y) and r'(t).
3.determine the derivative function (f o r)' by
3.1.differentiating the expression obtained in (1).
3.2.using the chain rule (theorem ) compare your answer.
A researcher is interested in estimating the average monthly salary of bank managers in NCR. He wants to be 90% confident that his estimate is correct. If the standard deviation is ₱8,500, how large a sample is needed to get the desired information and to be accurate within ₱1,150?
Calculate the equation for the plane containing the lines L1 and L2,where L1 is given by the parametric equation (x,y,z)=(1,0,-1)+t(1,1,1),t€R and L2 is given by the parametric equation (x,y,z)=(2,1,0)+t(1,-1,0),t€R.
6.
A multiple-choice test contains 10 questions. There are four possible answers for each question. b) In
how many ways can a student answer the questions on the test if the student can leave answers
blank?
The probability that Roy attends a practice session before a match is 95%. If he attends, the probability that he is chosen for the team which plays is 98%. If he does not attend, there is a 75% chance that he will be chosen for the team
a)Construct a well labeled tree diagram to represent all the possible outcomes. [4]
b) What is the probability that Roy:
i) attends practice and is chosen? [1]
ii) does not attend practice and is not chosen? [1]
iii) does not attend practice? [1]
iv) is chosen? [2]
