d. Consider another brand D of car tyres. It has been found that the probability that these car tyres which last longer than 40,000 km is 0.7. For samples of 36 tyres of brand D, P is the random variable of the sample proportion of these tyres which last longer than 40,000 km. i. Find the expected value and variance of P Find the probability that the sample proportion of these car tyres lies within two standard deviations of the mean. Give your answer correct to three decimal places. Do ii. not use a normal approximation.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Car tyres come in many different brands. Even on a car, the tyres can wear out after travelling different distances, due to cornering, braking and wheel alignment. Manufacturers of car tyres are interested in the average distance in kilometres travelled by tyres, or the lifetime of tyres until they are considered un-usable and need to be replaced. At this time a tyre is considered un roadworthy
d. Consider another brand D of car tyres. It has been found that the probability that these
car tyres which last longer than 40,000 km is 0.7. For samples of 36 tyres of brand D, P is
the random variable of the sample proportion of these tyres which last longer than 40,000
km.
i.
Find the expected value and variance of P
Find the probability that the sample proportion of these car tyres lies within two
standard deviations of the mean. Give your answer correct to three decimal places. Do
ii.
not use a normal approximation.
Transcribed Image Text:d. Consider another brand D of car tyres. It has been found that the probability that these car tyres which last longer than 40,000 km is 0.7. For samples of 36 tyres of brand D, P is the random variable of the sample proportion of these tyres which last longer than 40,000 km. i. Find the expected value and variance of P Find the probability that the sample proportion of these car tyres lies within two standard deviations of the mean. Give your answer correct to three decimal places. Do ii. not use a normal approximation.
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