Question 3 (10 marks) 

The probability that an electrical fuse, chosen at random from production, will be defective is 0.02. A random sample of 1000 fuses were tested.

 
(a) State the distribution of random variable x (1 mark)

(b) Show that the random variable x can be approximated to the normal distribution. (4 marks)

(c) Calculate the probability of observing 27 or more defectives. Interpret the probability value. (5 marks)

 
Question 4 (14 marks) 

A study is conducted to investigate the relationship between the cost of fire damage and the distance between the fire station and the location involves in the fire accident. The regression method is used to analyse the data in Table 3.
Table 3'. The estimated fire damage cost (RM million) and the distance (km)

Cost of Me damage     Distance
26.2            3.4
17.8            1.8
31.3            4.6
23.1            2.3
27.5            3.1
36.0            5.5
22.3            3.0
19.6            2.6
31.3            4.3
24.0            2.1
43.2            6.1
36.4            4.8 
26.1            3.8

(a) Identify the independent and dependent variables. (1 Mark)
(b) State the parameters for the simple linear regression model. (1 Mark)
(c) Calculate the correlation coefficient and interpret its value. (1 Marks)
(d) Find the equation of the best fit line of the simple linear regression model for the given data. (5 Marks)
(e) Estimate the distance between the fire station and the location of the fire incident if the estimated fire damage cost is RM50 million. (2 Marks)

Attachments: