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Cereal boxes are filled at a factory. Through extensive sampling, it is found that their equipment fills the boxes to a mean of 502 grams, with a standard deviation of 3.1 grams.
10,000 boxes of cereal are produced each day.
In a daily run, how many cereal boxes are expected to weigh between 500 and 504 grams?
The following contingency table represents the voters’ opinion concerning a new tax
reform bill and their level of income.
Levels of Income
Opinion Low Medium High
For 213 203 182
Against 138 110 154
Apply chi-square (χ2
) test to examine whether the opinion of people on new tax bill is
independent from their income level. [Table value of chi- square (χ2
) at 5% level of
significance and for 2 degrees of freedom is 5.99]
solve the equation for x belongs to R x/x-1 is equal to x + 1/x-2
Suppose p=0.9 and n=4 ,C={0000,1010,1100}.Compute pC,v where
v=1100
Give an example of a function of two variables such thatf(0,0) = 0 butfis NOT continuousat (0,0). Explain why the functionfis NOT continuous at (0,0).
Proof that an undirected graph has an even number of vertices of odd degree.
The early morning trading volumes (millions of shares) at Nairobi Securities Exchange for 18 days in January are as shown below. The probability distribution of trading volume is approximately normal. 216, 143, 221, 169, 198, 202, 210, 122, 187, 212, 232, 181, 199, 220, 258, 233, 219, 221. What is the probability that, on a randomly selected day, the early morning trading volume will be at most 189 million shares?
How many trading volumes should the company have to be in the top 35%?
Define Semigroup and Monoid. Show that the set of positive Integer is a monoid for the operation
defined by aOb = max{ a,b}.
Give an example of a function of two variables such that f(0,0) = 0 but f is NOT continuous at (0,0). Explain why the function f is NOT continuous at (0,0).
A Manufacturer produces two products, the Klunk and the Klick. Klunk has a contribution
to profit of $3, and the Klick $4 per unit. The manufacturer wishes to establish the weekly
production plan that maximizes profit. Production of these products is limited to machine,
labor and material constraints. Each Klunk requires four hours machining, four hours labor
and one kilogram of material, where as each Klick requires two hours machining, six hours
labor and one kilogram of material. Machining and labor has a maximum of one hundred
and one hundred and eighty hours available, and total material available is forty kilograms.
Because of a trade agreement, sales of Klunk are limited to a weekly maximum of twenty
units and to honor an agreement with an old established customer at least ten units of Klick
must be sold each week.
i. Determine graphically using linear programming a suitable production mix of Klunk
and Klick. [12]
ii. What will be the company’s maximum profit?
