Why might the following not be normally distributed? (a) The time it takes you to drive to the airport, (b) The annual income for a randomly chosen major league baseball player, (c) The annual hurricane losses suffered by homeowners in Florida.
I would be surprised on the hurricanes, some years are pretty mild
(a) The time it takes you to drive to the airport may not be normally distributed because there can be various factors that affect the travel time, such as traffic conditions, road construction, and weather. These factors can cause the distribution to be skewed or have outliers, making it deviate from a normal distribution.
(b) The annual income for a randomly chosen major league baseball player may not be normally distributed due to several reasons. Firstly, there can be outliers in the data because some players earn significantly higher salaries compared to others. Additionally, income in professional sports can be influenced by factors such as player performance, contract negotiations, endorsements, and team budget constraints, which can create a skewed or non-normal distribution.
(c) The annual hurricane losses suffered by homeowners in Florida may not be normally distributed because the occurrence and intensity of hurricanes can vary significantly from year to year. In years with no major hurricanes, losses may be close to zero, while in years with highly destructive hurricanes, losses can be extremely high. This leads to a distribution that is typically right-skewed, with a long tail on the higher end representing the significant losses.
There are several reasons why the following variables might not be normally distributed:
(a) The time it takes you to drive to the airport:
This variable is likely to have a skewed distribution rather than a normal distribution. There can be various factors affecting the driving time, such as traffic conditions, road construction, and accidents. These factors introduce variability and can lead to a non-normal distribution. For example, during peak hours, the driving time may be longer due to heavy traffic, resulting in a positively skewed distribution.
(b) The annual income for a randomly chosen major league baseball player:
The annual income of major league baseball players is often characterized by a few high-earning individuals and a majority of players with lower incomes. This type of distribution is called a "skewed distribution." The presence of a few outliers with significantly high incomes can cause the distribution to be positively skewed, meaning that the tail of the distribution extends further to the right.
(c) The annual hurricane losses suffered by homeowners in Florida:
The annual hurricane losses suffered by homeowners in Florida can be highly variable and unpredictable. The occurrence of hurricanes depends on various factors such as weather patterns and climate conditions. Additionally, the extent of damage caused by each hurricane can vary significantly, leading to a highly skewed distribution of losses. In this case, the distribution of hurricane losses is likely to be skewed to the right, with a long tail indicating a few extreme values.
To determine the actual distribution of these variables, you can collect data and visually examine the histogram or use statistical tests like skewness or kurtosis.
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However, I will start you out with a. There is a minimum time, with most of the trips near that time, but few times you might get caught in traffic jams, taking you much longer.