The manager of ERIZ Master of Construction company is examining the number of days (X) that a construction worker unable to work due to a bad weather condition during the monsoon season. TABLE 1 below shows the probability distribution of X.
TABLE 1
X 6 7 8 9 10 11 12 13 14
P(X = x) 0.03 0.08 0.15 0.20 0.19 0.16 0.10 0.07 0.02
i. Prove that the above distribution is a valid probability distribution of the random variable X.
(2 Marks)
ii. Construct the probability graph for the random variable X. (3 Marks)
iii. Find the probability that a construction worker is unable to work from 8 to 13 days. (2 Marks)
iv. Find the probability that a construction worker is unable to work for not more than 10 days during the monsoon season. (3 Marks)
v. Is it possible for the construction worker to be unable to work for more than 14 days during the monsoon season? Justify your answer. (2 Marks)
vi. Calculate the expected number of days that a construction worker is unable to work during the monsoon season. Interpret your answer. (3 Marks)
vii. Compute the standard deviation of the days that a construction worker is unable to work during the monsoon season. (4 Marks)
QUESTION 2 (9 MARKS)
A career woman decides to have children until she has her first girl or until she has three children, whichever comes first. Let X be the random variable of the number of her children.
i. Construct a probability distribution table for X. (6 Marks)
ii. Calculate the probability that she has at most TWO (2) children. (3 Marks)
QUESTION 3 (3 MARKS)
An importer is offered a shipment of jade jewelry for RM5,500. The probabilities that he will be able to sell it for RM8,000, RM7,500, RM7,000 or RM5,000 are 0.25, 0.46, 0.19 and 0.10 respectively. How much income can he expect to get from this jewelry shipment offer?
