Khan Academy Donate Gabrie \( 1^{\text {week }} \) Level 8 Combining normal random variables Google Classroom Microsoft Teams You might need: ? Catculator. Is Z table Sam and Taylor own and operate a car wash service. Sam cleans the interior of each car and Taylor cleans the exterior. The time it takes Sam to finish the interior has a mean of 20 minutes with a standard deviation of 6.4 minutes. The time it takes Taylor to finish the exterior has a mean of 18 minutes with a standard deviation of 4.8 minutes. Both of their finishing times are approximately normally distributed. Suppose we select a car at random, and define the random variable \( D \) as the difference between their finishing times. We can assume that their times are independent. Find the probability that they finish within 10 minutes of each other. You may round your answer to two decimal places. \[ P(|D|<10) \approx \] \( \square \) Show Calculator Related content \( \square \) Example: Analyzing distribution of sum of two normally distributed random variables \( \qquad \) Example: Analyzing the difference in distributions \( 9: 45 \) Do 4 problems
Added by Joel W.
Close
Step 1
- Let \( X \) be the time Sam takes to clean the interior, which is normally distributed with mean \(\mu_X = 20\) minutes and standard deviation \(\sigma_X = 6.4\) minutes. - Let \( Y \) be the time Taylor takes to clean the exterior, which is normally distributed Show more…
Show all steps
Your feedback will help us improve your experience
Jacob Fry and 72 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
On average, 120 minutes are required to complete and upload the answer booklet in an exam, with a standard deviation of 30 minutes. Answer following questions: i. What is the probability of completing the exam in 90 minutes or less? ii. What is the probability that a student will complete the exam in more than 80 minutes but less than 130 minutes? B. The air pollution resulting from factories, located near residential areas in big cities, is the main reason of asthma in people. 25 percent people in some factory area are asthmatic. Consider 220 people are residing in a factory area. Answer following questions: i. What is the expected number of asthmatic? ii. What is the probability that fewer than 30 people are asthmatic? iii. What is the probability that from 35 to 45 asthmatic? iv. What is the probability that 80 or more asthmatic? C. The average fee to attend a particular public sector university in a metropolitan area is $2,075 with a standard deviation of $640. Suppose a random sample of 80 students has been taken from this population. i. What is the value of the standard error of the mean? ii. What is the probability that the sample mean will be more than $1,175? iii. What is the probability that the sample mean will be within $1000 of the population mean? iv. How would the probability in part (iii) change if the sample size were increased to 110? D. The owners of the Metro Cash & Carry wished to study customers' shopping habits. From earlier studies, the owners were under the impression that a typical shopper spends 0.7 hour at the mall, with a standard deviation of 0.10 hour. Recently the owners added some specialty restaurants designed to keep shoppers in the mall longer. A research team was hired to evaluate the effects of the restaurants. A sample of 45 shoppers by the team revealed that the mean time spent in the mall had increased to 0.80 hour. i. Develop a hypothesis test to determine if the mean time spent in the mall changed. Use the .10 significance level. ii. Suppose the mean shopping time actually increased from 0.75 hour to 0.79 hours. What is the probability of making a Type II error? iii. When research team reported the information in part (b) to the mall owners, the owners believed that the probability of making a Type II error was too high. How could this probability be reduced?
Adi S.
Ivan K.
Frank D.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD