Math Answers

determine whether W={(x,y,z)/ x+y+z+1=0, x,y,z element of real number} is a subspace of R^3 or not?

Question 4 [25]

The amount of time devoted to preparing for a statistics examination by students is a normally

distributed random variable with a mean of 17 hours and a standard deviation of 5 hours.

Required:

a) What is the amount of time below which only 15% of all students spend studying?

b) What is the amount of time above which only one third of all students spend studying?

c) What is the probability that a student spends between 16 and 20 hours studying?

d) What is the probability that a student spends at least 15 hours studying?

e) What is the probability that a student spends at most 18 hours studying?

Question 3 [25]

Suppose that a mobile telecommunication company’s helpline receives five calls, on average, per

minute.

Required:

a) Discuss the difference between the Binomial probability distribution and the Poisson

probability distribution.

b) How many calls does the company expect to receive in a period of 30 minutes?

c) What is the probability that the company will receive at most four calls in a period of 4

minutes?

d) What is the probability that the company will receive at least three calls in a period of 5

minutes?

e) What is the probability that the company will receive between six and nine calls in a period

of 2 minutes?

A rectangular field is to be enclosed by a fence then subdivided into three areas by fences

parallel to the shorter side. Find the dimensions of the field with the largest total area that can be

enclosed with 260 m of fencing. What is the area?

The sum of two natural numbers is 18. If the product of one number with the square of the

other is a maximum, find the numbers.

For the given functions f (x), let x0 = 1, x1 = 1.25, and x2 = 1.6. Construct interpolation polynomials of degree at most one and at most two to approximate f (1.4), and find the absolute error.

a. f (x) = sin πx

b. f (x) =cube root of (x − 1)

c. f (x) = log₁₀ (3x − 1)

d. f (x) = e^2x − x

Direction: Answer the given problem.

The Guidance Counselor of your school claims that the Grade 11 students spend an average of 11.28 hours in a week doing performance tasks with standard deviation of 1.64. Your adviser thinks that students spend more time in doing performance tasks, so he decided to conduct his own research. He used a sample of 46 Grade 11 students and obtained a mean of 11.83. Is there enough evidence at 0.05 level of significance that the students spend 11.28 hours in a week doing performance tasks?

1.Find ∫cos^2 (2x)sin x dx

2.Find ∫(b − ax)e^4x dx . Give your answer in factor form.

Sketch a normal curve that has a mean of 60 and a standard deviation of 12. On the same x-axis, sketch another normal curve that has a mean of 90 and a standard deviation of 6. Describe the two normal curves.

Random samples of size 3 are taken from a population of the numbers 3, 4, 5, 6, 7, 8, and 9.

1. How many samples are possible? 

2. Construct the sampling distribution of the sample means.