I would like all parts for E, ( i, ii, iii, iv v, vi) to be answered please Car tyres come in many different brands. Even on a car, the tyres can wear out after travelling differentdistances, due to cornering, braking and wheel alignment. Manufacturers of car tyresare interested in the average distance in kilometres travelled by tyres, or the lifetime of tyres until they are considered un-usable and need tobe replaced. At this time a tyre is considered unroadworthy. E) The lifetime T in thousands of km of brand E of car tyres, satisfies a probability density function given by. f(t)=(at^2 0=t=50, b(100-t) 50=t=100, 0 elsewhere) i) Show that a = 3/312500 and b= 3/6250 ii) For 36 tyres of brand E, find the expected number that will last longer than 40,000 km. iii)Sketch the graph of T on the axes below, clearly labelling the scale. iv) Find the expected value and variance of brand E car tyres. v) Find the probability that the lifetime of brand E car tyres lies within two standard deviations of the mean. Give your answer correct to three decimal places. vi) Find the median lifetime of brand E car tyres. Give your answer correct to three decimal places
I would like all parts for E, ( i, ii, iii, iv v, vi) to be answered please
Car tyres come in many different brands. Even on a car, the tyres can wear out after travelling differentdistances, due to cornering, braking and wheel alignment. Manufacturers of car tyresare interested in the average distance in kilometres travelled by tyres, or the lifetime of tyres until they are considered un-usable and need tobe replaced. At this time a tyre is considered unroadworthy.
E) The lifetime T in thousands of km of brand E of car tyres, satisfies a probability density
i) Show that a = 3/312500 and b= 3/6250
ii) For 36 tyres of brand E, find the expected number that will last longer than 40,000 km.
iii)Sketch the graph of T on the axes below, clearly labelling the scale.
iv) Find the
v) Find the probability that the lifetime of brand E car tyres lies within two standard deviations of the mean. Give your answer correct to three decimal places.
vi) Find the
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