Analyzing Grades, Sales Campaigns & Car Mileage Stats

Statistics - CSW - Meinke Problem Set 1 Name__________________________ Problem Set Covers Lessons 6 to 9 Sections 3.1, 3.2 3.3, 3.4, 3.5, 4.1, 4.2, 4.3, 5.1, 5.2, 5.4, 6.1, and 6.2 in Openstax Introduction to Statistics This assignment is graded for correctness and will be included in the Test category of your grade. 45 points Instructions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. Your numerical answers must be written in context of the question with the appropriate units. When required, show the calculation of z-scores and draw and shade Normal Curve where appropriate. If you are using a function on your calculator or in Desmos to complete the calculation. Write the function and the parameters used. For example : If I use normalcdf on my calculator I will write normalcdf(lower:30, upper:50, : 32, : 4.2) = 0.68302 µ σ If i use normaldistr in Desmos I will write normaldist(32,4.2) min: 30, max: 50 = 0.68302 You may work with your classmates. You may ask for help from me during class or during ofʨice hours. You may not get help from anyone other than members of this class or me. 1. In some courses (but certainly not in an Introduction to Statistics course!), students are graded on a “Normal curve.” For example, students between 0 and 0.5 standard deviations above the mean receive a C+; between 0.5 and 1.0 standard deviations above the mean receive a B –; between 1.0 and 1.5 standard deviations above the mean receive a B; between 1.5 and 2.0 standard deviations above the mean receive a B+, etc. The class average on an exam was 60 with a standard deviation of 10. a. What is the lowest and highest grade that will earn a B. b. What is the proportion of students who will receive a B if the marks are actually Normally distributed? Sketch and shade a normal distribution curve.

2. From past experience, the owner of Paddy’s Sports Store finds that the mean number of Celtics hats sold in a sales campaign is 845, the standard deviation is 15, and a histogram of the demand is approximately Normal. The owner is willing to accept a 2.5% chance that the Celtics hat will be sold out. About how many Celtics hats should the owner order for an upcoming sales campaign? Sketch and shade a normal distribution curve. 3. Lamar is shopping for a used car, and he’s interested in determining the typical mileage on cars that are three or four years old. He looks at an online car-buying site and compares the number of miles on 30 cars that are three years old to 30 cars that are four years old. His results are summarized by Minitab below. All values are in thousands of miles. Descriptive Statistics: Mileage on Four year old cars in thousands of miles Sample size n=30 cars Mean 56.68 Standard deviation 17.82 Minimum 23.60 Q1 47.80 Median 54.70 Q3 64.50 Maximum 100.30 Descriptive Statistics: Mileage on Three year old cars in thousands of miles Sample size n=30 cars Mean 33.33 Standard deviation 12.70 Minimum 14.10 Q1 22.33 Median 32.10 Q3 39.23 Maximum 66.40 Both distributions are approximately Normally distributed. a. One car that Lamar is interested in is four years old and has been driven 40 thousand miles. Another one is three years old and has 30 thousand miles on it. How does the number of miles on these cars compare, relative to other cars of the same age? Provide appropriate statistical calculations to support your answer. (provide calculation work and 2 to 4 sentences)