Final answer:
The correct distribution to describe the cost of car maintenance is the exponential distribution with a mean of $150. To find the probability of costs exceeding $300, we use the CDF of the exponential distribution. Lastly, for exponential distributions, unlike normal distributions, the median is not equal to the mean.
Step-by-step explanation:
The cost of all maintenance for a car during its first year is best described by exponential distribution with a mean of $150. This is because the expenditure on maintenance could theoretically be any non-negative value, and the exponential distribution is used to model the time between events in a Poisson process, which in this case is the occurrence of maintenance costs. The exponential distribution is defined by the mean (average) time (or, in our case, cost) between events, whereas the normal distribution assumes a symmetric distribution of data around the mean, and the Poisson distribution models the number of events in fixed intervals of time or space.
To answer part f, which asks for the probability that a car required over $300 for maintenance during its first year, we would use the cumulative distribution function (CDF) for the exponential distribution. The formula for the CDF of an exponential distribution is 1 - e-(x/μ), where e is the base of the natural logarithm, x is the value for which we want to find the probability, and μ is the mean of the distribution. To find the probability that the cost exceeds $300, we calculate 1 - e-(300/150). The answer to part 104, which discusses distributions where the median is not equal to the mean, is B. Exponential.