QUESTION 1

1.1   The table shows the hourly wages (in Rs) received by a sample of 25 workers

36.50    39.50   40.00  42.50   38.00

36.00   38.50    39.50  40.80   39.60

38.80   42.60    40.50  35.50   40.50

37.80   40.60    41.00  41.50   41.80

39.00   39.50    40.50  38.50   37.50

(a) Calculate the following for the above data-

i) Mean

ii) Median

iii) Mode

iv) Range

v) Interquartile range

vi) Variance

vii) Standard deviation

viii) Coefficient of variation

(b) Construct a Box-and-Whisker plot

1.2 A firm pays a wage rate of Rs 30 per hour to unskilled workers, Rs 40 to semi-skilled workers and 50 to skilled workers. It employs 25 unskilled, 15 semi-skilled and 10 skilled workers. Using the number of workers in each category as weights, find the weighted average wage rate per hour paid by the firm

QUESTION 2

The table below shows the probability of a randomly selected employee, with respect to gender, occupation and university education, in a given organisation

a) Find the probability that the selected person has no university education

b) What is the probability that the person works in management?

c) Find the probability that the selected employee is male and has a university degree

d) What is the probability that the selected worker is a manager and has no university education?

e) What is the probability that the employee is employed in the management department or has university education?

f) What is the probability that the selected employee works in management or has no university education?

g) Find the conditional probability that the selected employee has no university education given that he is male

QUESTION 3

a) A chemical flow control device underfills 10% of all barrels. Using the Binomial distribution, find the probability that in a random sample of 5 barrels, the number of underfilled will be:

i) Exactly 3

ii) Zero

iii) At least 1

iv) At most 2

b) On average, 10 customers arrive at a takeaway every hour. Assuming the number of customers arriving follows a Poisson distribution, what is the chance that

i) 7 customers arrive in an hour?

ii) Less than 2 customers arrive in an hour?

QUESTION 4

a) Find the area under the standard normal curve

i) from z = 0 to z = 0.88

ii) between z = -1 to z = 1

iii) to the right of z = 2.55

iv) to the left of z = -1.60

v) from z = -1.60 to z = -2.55

b) Assume that family income are normally distributed with mean μ = Rs 16000 and standard deviation σ = Rs 2000. What is the probability that a family picked at random will have an income:

i) between Rs 15000 and 18000

ii) below Rs 15000

iii) above Rs 18000

QUESTION 5

a) A normally distributed population has a mean of 90 and standard deviation of 60. A random sample of 25 elements is selected from the population. Find the probability that the sample mean X is

i) less than 100

ii) between 100 and 150

iii) less than75

b) Explain the Central Limit Theorem.

c) A marketing researcher believes that the proportion of persons favouring a new package design is 0.6. Suppose that a sample of 100 persons is selected at random. Determine the probability that 70% or more of the persons selected will favour the new package.