Show transcribed image text 4. Tyres fitted to a certain off-road vehicle have a lifetime that is uniformly distributed over the interval 40 000 to 70 000 km. This fact is known to the manufacturer but not to the public. a) Sketch the probability density function of X. b) The manufacturer wants to guarantee that the tyres will last at least x km. What should x be so that at most 10% of tyres fail before x? c) Find the variance of tyre lifetime X. 2+2+2-6]
4. Tyres fitted to a certain off-road vehicle have a lifetime that is uniformly distributed over the interval 40 000 to 70 000 km. This fact is known to the manufacturer but not to the public. a) Sketch the probability density function of X. b) The manufacturer wants to guarantee that the tyres will last at least x km. What should x be so that at most 10% of tyres fail before x? c) Find the variance of tyre lifetime X. 2+2+2-6]
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