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A bus can accommodate a maximum of 60 passengers. If 𝑋 denotes the number of male
passengers, what are the possible values of 𝑋?
The monthly salaries of contract workers in a small Jamaican shipping company are approximately normally distributed with a mean of $60,000 and a standard deviation of $4,000. What percent of people earn less than $55,000?
A box contains 10 balls. Three are numbered 0, two are numbered 1, one is numbered 2, two are numbered 3, and two are numbered 4. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the standard deviation of the numbers on the balls. (Round off your final answer to 2 decimal places).
a) It has been estimated that 35% of all new employees of the WindThroft company have a first degree. In a sample of 10 new employees.
(i) What is the probability that exactly 4 of them have first degrees? [2 marks]
(ii) What is the probability that at least three (3) of them have first degrees? [8 marks]
(iii) Calculate the Mean, Variance and Standard deviation of the distribution [5 marks]
For the following differential equation locate and classify its singular points on the x-axis x^2 y" + (2-x)y' = 0.
Find a power series solution of xy'=y
Show that 𝑦=𝑐1𝑒𝑥+𝑐2𝑒2𝑥 is the general solution of 𝑦′′−3𝑦′+2𝑦=0 on any interval, and find the particular solution for which 𝑦 0 =−1 and 𝑦′(0)=1.
Define the functions of bounded variation. Show that if f is continuous on [a,b], and if 𝑓′ exists and is bounded in the interior, say 𝑓′(𝑥) ≤ 𝐴 for all 𝑥 in 𝑎,𝑏 ,then f is of bounded variation on [a,b].
If f is monotonic on [a,b], then show that f is of bounded variation on [a,b].
Based on the historical data, the population proportion of the residents who have generators in a subdivision is 80%. The local newspaper surveyed 20 residents and 9 claimed that they have generators. What is the correct value of test statistic?
