Final answer:
The question asks about sample sizes required for statistical analysis with skewed distributions and understanding the uniform and normal distributions. For skewed distributions, a sample size greater than 30 is typically needed to apply the normal model due to the Central Limit Theorem.
Step-by-step explanation:
The question involves understanding different statistical distributions and determining sample sizes for statistical procedures given the shape of the distribution and its parameters.
Part A
The random variable X signifies the time needed to change the oil on a car. It is uniformly distributed between 11 and 21 minutes.
Part B
The distribution is uniform, which means that every interval of the same length within the bounds of the distribution has the same probability as any other interval of the same length.
Part C
Graphing the distribution would result in a rectangle with a base extending from 11 to 21 minutes and a height determined by the uniform probability.
Part D
The probability P(x > 19) can be calculated using the properties of the uniform distribution.
Sample Size Selection
Given the right-skewed distribution mentioned, if the sample size is large enough (typically n > 30), the Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal regardless of the original distribution's shape. Therefore, letter C is the correct answer; the sample size needs to be greater than 30.
Understanding Distributions
For a distribution to be normal, the mean doesn't necessarily have to be significantly greater than the standard deviation, so this condition doesn't provide conclusive information about the type of distribution.
Estimating Time Needs
In estimating whether 1.1 hours per technician will be enough related to the preventive maintenance on air conditioners, the company should consider the mean and standard deviation of the service times, along with the size of the sample of units serviced.