Qualitative Analysis- Examination Revision Paper (Practice only)

Q1.

The numbers of cars breakdown in an expressway for a month is as follows:

30, 42, 28, 35, 20, 29, 33,25, 28, 31

(a) Find the mean, median and mode
(b) Calculate the variance and standard deviation
(c) Compute the quartiles
(d) Explain what are 'Descriptive Statistics' and 'Inferential Statistics'.

Q2.

(a) The daily number of the customers for a shop follows a binomial distribution. From record, 20% of the customers are male. On a particular day, 15 customers were being served.

Calculate the

i. probability of 3 customers are male
ii. probability that at most 2 customers are made
iii. mean number of male customers on that day

(b) A company receives an average of 1 complaint in a month. Find

i. the probability that exactly 2 complaints are received in a month
ii. the probability that at most 2 complaints in a month,

Q3.

A certain brand of yogurt is packed in tubs with masses that are normally distributed with mean of 1kg and a standard deviation of 50g.

(a) Find the probability that a randomly selected tub weighs

i. More than 950g
ii. Between 950g and 1100g

(b) A box contains 20 such tubs. What is the probability that the mean mass for a tub is between 980g and 1030g?

Q4.

(a) The production machines of a company produce metal discs of 200g. It is noted that the weight of the discs follows a normal distribution a standard deviation of 7g. To test the consistency of the machines, 50 discs are randomly selected and the mean weight is 250g. What is the 99% confidence interval for the average weight of the selected discs?

(b) A machine produces metal discs with a diameter of 12cm. The diameter of discs need to be exactly 12cm with only a small variation of 2%. On a particular, the manufacturing manager measured the diameters of 50 discs and noted that the mean is 11.5cm. It is assumed that the diameters of discs are normally distributed with a standard deviation of 1.8cm. Conduct a hypothesis testing using the critical value approach, at the 0.1 level of significance. Is there evidence that the machine is not producing the discs at the specified diameter of 12cm?

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