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Question 4(1\" marks} {a} An assessment was made to measure the life expectancy of nine bread-making machines. Based on the assessment, the mean life expectancy is seyen years. with a standard deviation of one year. [i] Calculate the probability that the life expectancy of a randomly selected bread- makjng machine falls between 6.4 and 12 years. {3 marks] (ii) Based on a{i), how many machines are expected tn have life expech between 15.4 and 12 years? {1 mark} ASSESSMENF 2 STA 415 (b) Suppose that some batch of tires of the same type are obtained from an ongoing production process with mean SID-[l and standard deviation 100. (i) What is the probability that not more than 35d tires will be defectiye? {3 marks] {ii} The production will be stopped for a maintenance if the number of defective tires produced reached the upper l% of production. What is the maximum number of defective tires production allowed before the production need to be stopped? {3 marks] Question 5 (5 marks) A group of medical students want to see if there is a relationship between height and pulse rate of hospital patients. The height of the patient is in cm and the pulse rate of the patient in beats per minute. There are 50 patients randomly selected and were summarize as follows. 50 50 50 Ex, = 8436, Ey. = 4115, x," = 1427556, =342577, Exy = 695171 i=1 (a) Compute the correlation coefficient for the above data. (4 Marks) (b) What can you conclude from the value of the correlation coefficient obtained from part (a)? (1 Mark)