School of Engineering 45770 Dr Riaz Akhtar 4. (e) probability that: (1) There ar

Question

School of Engineering 45770 Dr Riaz Akhtar 4. (e) probability that: (1) There are exactly zeto defects in a 50 m length of cable. Gi) There are three or fewer defects in a 100 m length of cable. In a fibre optic cable, it is known that there are on average 1.5 defocts per S0 m. What is the 8 marks (b) Six different types of defect are found in the cables. The chance of cach defect occurring is ually likely. Fifty components are selected at random and the number of defects in each of the components was recorded ire lease Defect Number 14 8 4 of defects 12 Determine if the expected patterm of defects has been obtained using a significance level of p- 0.05. 12 marks (c) The probability of a defect in a fibre optic cable reel supplied by a different manufacturer is 0.1. Determine the probability of two reels being defective out of a batch of twenty. S marks] Page 5 of 7

Explanation / Answer

Since the chance of getting each defect is equally likely, we can assume a null hypothesis for the distribution.

Significance level of p =0.05

Probability of the distribution should be more than 0.05 to become insignificant and hence the hypothesis will not be rejected, or we can say that the expected pattern of defects has been obtained.

Probability of getting any defect = 1/6

From the above distribution,

P(Defect 1) = 14/50 = 0.28 > 0.05

P(Defect 2) = 8/50 = 0.16 > 0.05

P(Defect 3) = 4/50 = 0.08 > 0.05

Since the least probability is even greater than the significance value.

We can say that the expected pattern of defects has been obtained.

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