The wait time in a Drs office is uniformly distributed from 14 minutes to 34 minutes. Using this information about a uniform distribution answer the following questions: (No Rounding) Chris OByrne 2024A. What is the probability that your wait time will be between 22 and 31 minutes?B. What is the probability that your wait time will be at least 20 minutes?C. What is your expected wait time in the Drs office? The average monthly car expense for an Uber/Lyft driver is $627 with a standard deviation of $143. These monthly car expenses are normally distributed. Use this information to answer the following questions: (*Must use values from z-table (back of CH6 notes) or you will not receive credit) Chris OByrne 2024A. What is the percentage of monthly car expense that will be less than $525?B. What is the percentage of monthly car expense that will be at least $400?C. What is the percentage of monthly car expense that will be between $750 and $1,000?D. Where do the top 11% (longest/Highest) of monthly car expenses begin? (no rounding answer) Share on Facebook Tweet Follow us Sample Answer Essay on Probability Distributions in Healthcare and Transportation Costs Introduction In the realm of statistics and probability, understanding different types of distributions is crucial in various fields. In this essay, we will delve into two types of distributions: uniform distribution in healthcare wait times and normal distribution in monthly car expenses for Uber/Lyft drivers. By exploring these concepts, we can gain insights into the probabilities associated with each scenario. Uniform Distribution in Healthcare Wait Times A uniform distribution is characterized by constant probability, where all intervals of equal length have an equal probability of occurrence. Let’s apply this concept to the scenario of wait times in a doctor’s office, where the wait time ranges uniformly from 14 minutes to 34 minutes. A. Probability of Wait Time Between 22 and 31 Minutes To find the probability that the wait time falls between 22 and 31 minutes, we calculate the proportion of the interval length to the total length of the distribution: [ P(22 leq X leq 31) = frac{31 – 22}{34 – 14} = frac{9}{20} = 0.45] Thus, there is a 45% probability that the wait time will be between 22 and 31 minutes. B. Probability of Wait Time at Least 20 Minutes To determine the probability of waiting at least 20 minutes, we compute the proportion of the interval from 20 minutes to 34 minutes: [ P(X geq 20) = frac{34 – 20}{34 – 14} = frac{14}{20} = 0.70] Therefore, there is a 70% chance that the wait time will be at least 20 minutes. C. Expected Wait Time in the Doctor’s Office The expected value or mean of a uniform distribution is given by the average of the minimum and maximum values: [ text{Expected Wait Time} = frac{14 + 34}{2} = 24 text{ minutes}] Hence, the expected wait time in the doctor’s office is 24 minutes. Normal Distribution in Monthly Car Expenses for Uber/Lyft Drivers Normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve. Let’s explore this distribution in the context of monthly car expenses for Uber/Lyft drivers, with an average expense of $627 and a standard deviation of $143. A. Percentage of Expenses Less Than $525 To find the percentage of monthly car expenses less than $525, we need to standardize the value using z-scores and refer to the z-table: [ Z = frac{525 – 627}{143} = -0.7133] By looking up the z-table, we find that the percentage is approximately 24.66%. B. Percentage of Expenses at Least $400 Similar to the previous calculation, we standardize $400 and find: [ Z = frac{400 – 627}{143} = -1.5874] Referring to the z-table, we get around 5.32% for expenses equal to or exceeding $400. C. Percentage of Expenses Between $750 and $1,000 By standardizing $750 and $1,000, we calculate: [ Z_{750} = frac{750 – 627}{143} = 0.86] [ Z_{1000} = frac{1000 – 627}{143} = 2.60] From the z-table, the percentage falls between these values is approximately 28.07%. D. Starting Point for Top 11% of Monthly Car Expenses To determine where the top 11% of expenses begin, we refer to the z-table for the corresponding z-score: [ Z_{11%} approx 1.22] We then reverse standardize this score to find the starting point: [ X = Z_{11%} times 143 + 627] Therefore, the top 11% of monthly car expenses begin around $818. Conclusion Understanding probability distributions is crucial in making informed decisions and predictions in various scenarios. By applying concepts from uniform and normal distributions to healthcare wait times and transportation costs, we can analyze probabilities effectively and derive meaningful insights for decision-making. This question has been answered. Get Answer
