Math Answers

Q. Use Runge Kutta Fehlberg method with tolerance TOL=〖10〗^(-6), hmax=0.5, and hmin=0.05 to approximate the solutions to the following initial value problem. Compare the result to the actual value.
y^'=(t+〖2t〗^3)y^3-ty, 0≤t≤2,y(2)=1, y(0)=1/3 , actual solution y(t)=〖(3+2t^2+6e^(t^2 ))〗^(-1⁄2)

Q. Use Runge Kutta Fehlberg Algorithm with tolerance TOL=〖10〗^(-4) to approximate the solution to the following initial value problem.
y^'=sint+e^(-t), 0≤t≤1,y(0)=0,with hmax=0.25,and hmin 0.02

Q. Use Runge Kutta Fehlberg method with tolerance TOL=〖10〗^(-4), hmax=0.25, and hmin=0.05 to approximate the solution to the following initial value problem. Compare the result to the actual value.
y^'=1+〖(t-y)〗^2, 2≤t≤3,y(2)=1, actual solution y(t)=t+1⁄((1-t)).

Find the nearest neighbor statistic when n points are equidistant from one another on the circumference of a circle with a radius r, and there is one additional point located at the center of the circle. Assume that travel between neighboring points on the circumference can only occur along the circumference. Note that you can break the solution into two parts - one where the distance between neighboring points along the circumference is less than r, and the other where the distance is greater than or equal to r.

Describe two situations that can be modelled with a tree . Describe the graph model that you will use

4.1 A discrete random variable can be described by the Binomial distribution if it satisfies four conditions. List each of these conditions. (4 marks)
4.2 Statistics show that 40% of Zimbabweans adults drink beer. If six Zimbabweans adults are randomly selected,
calculate the probability that four drink beer. (5 marks)
4.3 The average mark (in percentage) for an Economics test comprising of 300 students is 54%. If the marks are normally distributed with a standard deviation of 8%, determine the number of students with a mark over 70%.
(5 marks)
4.4 Differentiate between the following terms as used in statistics:
4.4.1 Ordinal Scaled data and Nominal-scaled data (2 marks)
4.4.2 Discrete Data and Continuous data (2 marks)
4.4.3 Observation and experimentation (2

4.1. A discrete random variable can be described by the binomial distribution if it satisfies four conditions. State
these FOUR (4) conditions. (4 marks)
4.2. The pass rate for a Statistics test in a class of MBA students is 65%. If five students are randomly selected from
the class, determine the probability that at least two passed the test. (7 marks)
4.3. Explain why the areas for only positive z-values are given on a standard normal distribution table. (2 marks)
4.4. The weight of a packet of imported biscuits from a shipment is normally distributed with a mean of 500 g and a
standard deviation of 40 g. What percentage of packets of the shipment weighs between 540 g and 560 g?
(5 marks)

4.1 A discrete random variable can be described by the Binomial distribution if it satisfies FOUR (4) conditions. State these conditions. (4 marks)
4.2 A shoe factory in Umlazi in the district of Durban shows that 30% of customers use a credit card to make payment. On a particular morning, 7 customers purchase shoes from the store. Determine the probability that;
4.2.1 3 customers will pay by credit card. (4 marks)
4.2.2 At least one will pay by credit card. (4 marks)
4
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4.3 The time it takes a randomly selected job applicant to perform a certain task is normally distributed with a mean value of 120 seconds and a standard deviation of 20 seconds. Determine the probability that a randomly selected candidate will complete the task;
4.3.1 between 100 and 130 seconds. (3 marks)
4.3.2 between 75 and 100 seconds. (3 marks)
4.3.3 within 75 seconds. (2 marks)

Two balls of same colour are put into second box from first box.Then a ball is raised from the second box and it is seen red.What is the probability that rhe red ball was in the first box?

A population has a mean of 220 and a standard deviation of 80. Suppose a sample of size 100 is selected and x ̅ is used to estimate μ.

What is the expected value of x ̅ ?






What is the standard deviation of x ̅?







What is the probability that the sample mean will be within ± 5 of the population mean?








What is the probability that the sample mean will be within ± 10 of the population mean?