Final answer:
The choice of probability distribution to analyze how long automobile owners plan to keep their cars depends on the context, with options like normal, binomial, and uniform distributions based on the characteristics of the data.
Step-by-step explanation:
When deciding on a probability distribution to analyze how long automobile owners plan to keep their cars, the context of the question usually guides the choice. If we're looking at a specific time frame that owners keep their cars, and that data is normally distributed with mean and standard deviation, the normal distribution would be suitable. However, if we are interested in the count of events, like the number of owners who keep their cars for less than a specified period or until a certain event occurs, the binomial distribution might be more appropriate. In contrast, if car ownership lengths are evenly spread across a range, the uniform distribution fits best. But, with non-symmetric data where the mean and median are not equal, the exponential distribution could be considered.
For example, given that the time owners keep their cars is normally distributed with a mean of seven years and a standard deviation of two years, (as mentioned in Chapter 11), the normal distribution would be the one to use for analysis involving individual ownership lengths (question 102). In contrast, if we are analyzing the probability of a certain outcome from a large number of trials, his could involve a binomial distribution (question 100). Additionally, the uniform distribution is applicable when analyzing the uniformly distributed ages of cars in a parking lot (question 39).
Each distribution requires different parameters. For the normal distribution, the mean (μ) and standard deviation (σ) are required, whereas for the binomial distribution, the sample size (n) and the probability of success in a single trial (p) are needed. For the uniform distribution, we define the minimum and maximum values of the random variable X representing the range of car ages.