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Marks of 12 students in Arithmetic and Algebra are given below:
Arithmetic 60 34 40 50 45 40 22 43 42 66 64 46
Algebra 75 32 33 40 45 33 12 30 34 72 41 57
Calculate the rank correlation coefficient
QUESTION 1 (15 MARKS)
In a butter-packing factory, the quantity of butter packed in a day using a certain
machine is normally distributed. In a particular day, 12 packets of butter were taken at
random from this production line, and their masses, measured in grams, were:
9.50 9.50 11.20 10.60 9.90 11.10
10.90 9.80 10.10 10.20 10.90 11.00
By using these measurements:
a. Point out the estimator that is used to estimate the mean parameter.
[ 3 marks ]
b. Explore the 95% confidence interval for the mean mass produced by this
machine. [12 marks ]
[Total : 15 marks]
It has been found that one out of every four people who visit a retail website make a purchase worth R500 or more. If we randomly select a sample of 5 visitors to the website, what is the probability that less than one of the visitors will make a purchase worth R500 or more?
three cards are drawn in succession from a deck without replacement. find the probability distribution for the number of hearts
An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 800 hours and a standard deviation of 40 hours. Find the probability that a bulb burns between 778 and 843 hours.
The owner of a small hotel with 5 rooms is considering buying TV sets to rent to room occupants.
He expects that about half of his customers would be willing to rent sets and finally he buys 3 sets.
Assuming 100% occupancy at all times
i) What fraction of evenings will there be more requests than TV sets?
ii) What is the probability that a customer who requests a TV set will receive one?
A bank provides two different kind of bank account: current accounts and savings accounts. Every bank customer has one or both of these. 90% of bank customers have current accounts and 60% of bank customers have savings accounts. If a customer is chosen uniformly at random from the set of all bank customers, calculate the following probabilities, showing your working in each case:
The concept of conditional probability
A computer has contracted a virus that spreads through email. Alice, the user of this computer has 50 friends: each day she picks one friend randomly (i.e. with equal probability p = 1/50 ) and sends him an email which unfortunately contains the virus.
How many days (on average) will it take until all 50 friends are infected?
(Note that the same user can be picked)
