1. Packages delivered from a local distribution center to their final destination vary between 30 and 240 minutes, and follow a uniform distribution. a. What is the expected value of time it takes for parcels to arrive at their final destination.b. What is the probability that a package takes 60-120 minutes to arrive?c. What is the likelihood that a package takes more than 200 minutes?d. What is the probability that a package takes less than 100 minutes?2. A fleet of vehicles requiring regular maintenance typically cost $980 per month, with a standard deviation of $100, and follow a normal distribution. Two repairs completed recently, costing $1093 and 937, are being assessed to see if the costs are comparable to typical costs. Compute the z-value for each of these costs and comment on the value relative to typical costs.3. The income for mid-level executives is normally distributed, with a mean of $110,000 and standard deviation of $18,000. a. What is the probability of finding an executive whose income is greater than $125,000? b. What is the likelihood of finding an executive who income is less than $115,000? c. What is the probability of finding an executive who income is between $100,000 and $110,000?4. A retail store maintains inventory so that the likelihood of running out of stack (i.e. a stock out) is 5%. If the store anticipates demand for an item to be 10 units per month, with a standard deviation of 1, how many units should be kept in stock? Assume demand is normally distributed, and round your answer to the nearest whole number that ensures stock outs occur no more than 5% of the time.

Week 3 Project - STAT 3001 Student Name: <Type your name here> Date:<Enter the date on which you began working on this assignment.> Instructions:To complete this project, you will need the following materials: STAT DISK User Manual (found in the classroom in Doc Sharing)Access to the Internet to download the STATDISK program. Part I.Analyze Data Instructions Answers Open the file Car Measurements using menu option Datasets and then Elementary Stats, 13th Edition.This file contains information on a number of measurements related to cars. How many observations are there in this file? 2-5 Analyze the data in this file and complete the following table, indicating for each variable what type of data it represents. Variable Qualitative/ Quantitative Discrete/ Continuous/ Neither Level of Measurement Size Braking (distance) City (MPG) Car 6. Would you consider this data to represent a sample or a population? Why? Part II. ScatterPlots 7. Create a scatterplot for the data in the Length (inches) and Braking distance (feet) columns.Paste it here.You may need to resize the plot once it is in this file. 8. Explain the visual relationship between Length and Braking distance. 9. Create a scatterplot for the data in Displacement (liters) and Highway (MPG) columns. Paste it here. You may need to resize the plot once it is in this file. 10. Explain the visual relationship between Displacement and Highway MPG. Part III.Correlation 11.Using Stat Disk, calculate the linear correlation between the data in the Length and Braking distance columns. List the steps used for the calculation and give the resulting correlation coefficient. 12.Explain the mathematical relationship between Length and Braking distance based on the linear correlation coefficient.Be certain to include comments about the magnitude and the direction of the correlation. 13.List the sample size and the degrees of freedom for this computation. 14.Using Stat Disk, calculate the linear correlation coefficient between the data in the Displacement and Highway MPG columns. 15.Compare and contrast these two relationships: Length and Braking distance Displacement and Highway MPG How are they similar? How are they different? [Hint: Read Page 290 “Types of Correlation”] Part IV.Simple Regression Let’s say that we wanted to be able to predict the city MPG of a car based on its Weight in pounds. Using this sample data, perform a simple-linear regression to determine the line-of-best fit. Use the Weight as your x (independent) variable and City MPG as your y (response) variable. Use 3 places after the decimal in your answer. Refer to page 13 in the Stat Disk User’s Manual. 16. Paste your results here: Answer the following questions related to this simple regression 17. What is the equation of the line-of-best fit?Insert the values for bo and b1 from above into y = bo + b1x. 18. What is the slope of the line?What does it tell you about the relationship between the Weight and City MPG data? Be sure to specify the proper units. 19.What is the y-intercept of the line?What does it tell you about the relationship between Weight and City MPG? 20. Using the regression equation, what would you predict for the City MPG of a car weighing 2250 pounds? Show your calculation and round to the nearest tenth. 21. Using the regression equation, let’s say you have a car with a City MPG of 29, what would the car weigh? Round to the nearest whole number. 22. Find the coefficient of determination (R2 value) for this data.What does this tell you about this relationship? [Hint:see definition on Page 311.] Part V.Multiple Regression Let’s say that we wanted to be able to predict the Highway MPG of a car based on DisplacementLengthBraking Using this sample data, perform a multiple-regression using Displacement, Length, Braking distance with Highway MPG as the dependent variable. Refer to page 14 in the Stat Disk User’s Manual. 23. Paste your results here: 24. What is the equation of the line-of-best fit?The form of the equation is Y = bo + b1X1 + b2X2 + b3X3 (fill in values for b0, b1, b2, and b3). [Round coefficients to 2 decimal places.] 25. Using the multiple regression equation, what would you predict for the Highway MPG of a car whose Length in inches is 184Braking distance in feet is 139Displacement in liters is 2.2 Round to the nearest tenth. 26. What is the R2 value for this regression?What does it tell you about the regression? Submit your final draft of your Word file by going to Week 3, Project, and follow the directions under Week 3 Assignment 2.Please use the naming convention "WK3Assgn2+first initial+last name" as the Submission Title.