In September 2024
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A government agency was charged by the legislature with estimating the length of time it takes citizens to fill out various forms. Two hundred randomly selected adults were timed as they filled out a particular form. The times required had mean 12.8
minutes with standard deviation1.7 minutes. Construct a 90%
confidence interval for the mean time taken for all adults to fill out this form.
A magazine reported that 3% of Turkish drivers smoke while driving. If 300 drivers are selected at random,
find the probability that 4 or 5 drivers accept that they smoke while driving. Use all possible calculation methods
and justify them with sufficient explanation.
Distributed system is described as scalable when it remains effective when there is a
significant increase in the number of resources and the number of users. However, these
systems sometimes face performance bottlenecks.
How can these be avoided?
A University department has a file called exam marks which contains a list of
examination marks indexed by student names in alphabetical order. A student manages
to access the exam marks file. The student cannot read the file since it is encrypted.
However, they can work out the position of their own mark making use of the fact that
the students are listed in alphabetical order. The student swaps their mark with that of
the student who is always ‘top of the class’.
Write a paragraph discussing which of the security features has been breached?
The reaction time of a driver to visual stimulus is normally distributed with a mean of 0.4
seconds and a standard deviation of 0.05 seconds. Use R to find the
(a) probability that a reaction requires more than 0.5 seconds.
(b) probability that a reaction requires between 0.4 and 0.5 seconds.
Question: 1
The probability that an individual suffers a bad reaction from injecting Covid-19 vaccine is 0.003,determine the probability that out of 4000 individuals
(i) Exactly 2 individuals will suffer a bad reaction.
(ii) More than 4 individuals will suffer a bad reaction
Question: 2
If 20% of the bolts produced by a machine are defective. Determine the probability that out of four bolts chosen at random, at most 2 bolts will be defective.
what is the role of the 2 metal ions in DNA polymerase
You are a prospective entrepreneur in SA. Develop a tourism product/service/concept that is exceptionally creative/unique. Identify a name and design a logo as well as a slogan for your product/service/concept. Describe
your product/service/concept in detail and where applicable, make use of graphic representations/ photo’s.
Consider a firm with the following production function 𝑸 = 𝟓𝟎𝟎𝟎𝑳 − 𝟐𝑳 𝟐
a. How many units of labor are needed at that point.
b. Obtain the function of marginal product of labor (𝑀𝑅𝐿).
c. Graph the production function and the 𝑀𝑅𝐿.
Consider the following supply and demand schedule of wooden tables.
a. Draw the corresponding graphs for supply and demand.
b. Using the data, obtain the corresponding supply and demand functions.
c. Find the market-clearing price and quantity.
Price per thousand Supply Demand
2 96 110
4 196 190
6 296 270
8 396 350
10 496 430
12 596 510
14 696 590
16 796 670
18 896 750
20 996 830
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