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Obtain the directional derivative for a scalar field phi(x, y, z) = 3(x^2)y - (y^3)(z^2) at the point (1, -2, -1) in the direction i^cap+j^cap+k^cap.
Use the mean value theorem to show that x < sin-¹x , for x > 0
The height of students in a school is normally distributed with mean 138 centimetres and standard deviation equal to 15 centimetres. What is the minimum height of a student such that P(X≥x) = 0.0548?
Question 2
(a) It is noted that 8% of Kaplan students are left handed. If 20 (TWENTY) students are randomly
selected, calculate the
i. probability that none of them are left-handed, (2 marks)
ii. probability that at most 2 are left-handed, (3 marks)
iii. standard deviation for the number of left-handed students (2 marks)
(b) If 50 (FIFTY) classes of 20 (TWENTY) students are randomly selected, what is the probability that 10
(TEN) classes have no left-handed students?
(a) It is noted that 8% of Kaplan students are left handed. If 20 (TWENTY) students are randomly
selected, calculate the
i. probability that none of them are left-handed, (2 marks)
ii. probability that at most 2 are left-handed, (3 marks)
iii. standard deviation for the number of left-handed students (2 marks)
(b) If 50 (FIFTY) classes of 20 (TWENTY) students are randomly selected, what is the probability that 10
(TEN) classes have no left-handed students?
Question 1
a) The following data represent the number of years patients survived after being diagnosed with
terminal cancer:
0.4, 0.5, 0.6, 0.6, 0.6, 0.8, 0.8, 0.9, 0.9, 0.9,
1.2, 1.2, 1.3, 1.4, 2.1, 2.4, 2.5, 4.0, 4.5, 4.6
(i) Construct a stem-and-leaf display (6 marks)
(ii) Supposedly you are inserting the above stem-and-leaf display in a report to be
submitted to management, write a short comment on the diagram.
(4 marks)
b) The following data shows the weight (in kg) of 13 crabs found in a restaurant on a particular evening:
3.4 1.2 1.7 2.4 2.4 1.1 0.9 0.8 1.2 1.6 0.7 1.2 1.3
(i) Compute the mean and median. (3 marks)
(ii) Determine the shape of the distribution based on the sample data. Explain your
conclusion. (2 marks)
a) The following data represent the number of years patients survived after being diagnosed with
terminal cancer:
0.4, 0.5, 0.6, 0.6, 0.6, 0.8, 0.8, 0.9, 0.9, 0.9,
1.2, 1.2, 1.3, 1.4, 2.1, 2.4, 2.5, 4.0, 4.5, 4.6
(i) Construct a stem-and-leaf display (6 marks)
(ii) Supposedly you are inserting the above stem-and-leaf display in a report to be
submitted to management, write a short comment on the diagram.
(4 marks)
b) The following data shows the weight (in kg) of 13 crabs found in a restaurant on a particular evening:
3.4 1.2 1.7 2.4 2.4 1.1 0.9 0.8 1.2 1.6 0.7 1.2 1.3
(i) Compute the mean and median. (3 marks)
(ii) Determine the shape of the distribution based on the sample data. Explain your
conclusion. (2 marks)
(a) Superior Construction Pte Ltd is a successful company dealing with many major projects in
Singapore. Recently, it has submitted its biddings for two major Government projects. Project A
worth about $120 million and the company believes it has 40% chance of securing the project.
Project B worth $1.8 billion and there is 30% chance the company can win the project. Both projects
are independent of each other. What is the probability that the company:
i. will secure Project A or B but not both (3 marks)
ii. will not secure Project A or will not secure Project B (3 marks)
(b) Do you agree that “if two events are mutually exclusive then these two events will be independent”?
Why? (5 marks)
(c) Provide one business-related example each, with explanation, for mutually exclusive and
independent events. (4 marks)
Singapore. Recently, it has submitted its biddings for two major Government projects. Project A
worth about $120 million and the company believes it has 40% chance of securing the project.
Project B worth $1.8 billion and there is 30% chance the company can win the project. Both projects
are independent of each other. What is the probability that the company:
i. will secure Project A or B but not both (3 marks)
ii. will not secure Project A or will not secure Project B (3 marks)
(b) Do you agree that “if two events are mutually exclusive then these two events will be independent”?
Why? (5 marks)
(c) Provide one business-related example each, with explanation, for mutually exclusive and
independent events. (4 marks)
Use the power series method to obtain one solution of the following ODE:x^2y"+3y'-xy=0
Sketch the graph of the function f defined by 4 3 f(x) = x + 8x , clearly giving all the
properties used in it.
properties used in it.
A random sample of 700 units from a large consignment showed that 200 were damaged. Find
95% confidence interval for the proportion of damaged unit in the consignment.
95% confidence interval for the proportion of damaged unit in the consignment.
Obtain a unit tangent vector to any point on the curve defined by the parameteric equations: x = sin 3t, y = 2cos 3t, z = 4t.
