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According to internal testing done by the Get-A-Grip tyre company over many years, the mean lifetime of tyres sold on new cars is normally
According to internal testing done by the Get-A-Grip tyre company over many years, the mean lifetime of tyres sold on new cars is normally distributed with a mean of 37,000 kilometres and a standard deviation of 4,000 kilometres.
a) What is the probability of a random new car with these tyres lasting for 40,000 km or more? If this is true, then we would like to know what mean kilometres of tyre-lifetimes are likely to occur for the university's fleet of 100 such cars (a random sample of the new cars involved).
b) If the claim by Get-A-Grip is true, what is the mean of the sampling distribution of (x-bar) for samples of size n = 100?
c) If the claim by Get-A-Grip is true, what is the standard deviation of the sampling distribution of (x bar) for samples of size n = 100?
d) Sketch this sampling distribution.
e) What is the probability that such a sample of 100 cars would have an average kilometres of tyre-lifetimes greater than 40,000km?
f) If the population distribution was really skewed and not Normal, EXPLAIN whether or not these probability calculations on the sample of 100 cars still validly be done. State the concept or theory that is involved in this situation.
g) On the same sketch in part d) above sketch the distribution that would result for the same population if the sample size was n = 400.
