ANTH question

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Q3 AND Q5

3. The lifetime (in hours) X of a certain electrical component follows an exponential distribution with parameter λ = 0.001. Three of these components operate independently in a system. The system fails if at least two of the components fail. Find the probability that the system operates for at least 200 hours without failure.

5. The heights of male students entering the University of Hong Kong, X, are normally distributed with a mean of 170.4 cm. It is known that about 2.5% of the students are taller than 190 cm.

(a) What is the standard deviation of X?

(b) What is the proportion of male students at the University of Hong Kong with a height of 160 cm or less?

(c) What is the probability that the mean height of n = 4 randomly selected male students exceeds 175 cm?

(d) Male students are randomly selected one after the other. What is the probability that the fifth selected student is the second selected student with a height below160 cm?