3 Statistics Questions

Mathematics

Civil Engineering

UNISA

### Question Description

I'm working on a statistics question and need a sample draft to help me study.

Hi. I am having trouble to understand the questions. Please help me with the following statistics questions. I need it done ASAP please

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1) Abiding by Covid19 restrictions my local quilt shop is hosting a free seminar on the use of Studio 180 tools. Attendance will require a reservation but they also expect a certain number of noshows. The Saturday morning class has room for 26 attendees. From this past Spring and Summer events we’ve seen that if 30 tickets are reserved for the class, then the probability distribution for the number who actually show up for the class is as shown in the table below: Number who actually show 22 23 24 25 26 27 28 29 30 Probability 0.16 0.22 0.2 0.14 0.11 0.04 0.08 0.04 0.01 Assume that 30 attendees have reserved a seat for this quilting class (a) There are 26 seats available in this classroom. What is the probability that all students who show up for this class will get a seat? (b) Given that not all seats in this class are filled, what is the probability that only 23 students show up for the class? 2) Quilts-on-the-Corner is considering purchasing a new HQ longarm quilting machine or a GL longarm quilting machine(LAQ) . The HQ LAQ costs \$29,800 and the GL LAQ costs \$30,500. Quilts-onthe-Corner replaces their longarm quilting machines every five years. The 5-year repair contract for the HQ costs \$50 per month and covers an unlimited number of repairs. The repair for the GL costs \$150 per repair. The GL has a maintenance cost of \$65 per year. Based on past performance, the distribution of the number of repairs needed over any one-year period for the GL is shown below: Number of Repairs 0 1 2 3 4 Probability 0.29 0.4 0.13 0.12 .06 You are asked to give a recommendation based on overall cost as to which longarm; HQ or GL, along with its repair contract, should be purchased. What would your recommendation be? Give a statistical justification to support your recommendation. 3) Quilts-on-the-Corner LAQ department needs to completely longarm 33 quilts during each 8 hour shift. The manager needs to know the total amount of LAQ time for the 33 quilts so that time can also be scheduled for breaks during a shift. Quilt tops vary by size and complexity. The distribution of the longarm quilting time, in minutes, is roughly symmetric with a mean quilting time length of 12.9 minutes and a standard deviation of 18.1 minutes. a) Describe the sampling distribution of the sample mean quilting time for random samples of 33 quilt tops at Quilts-on-the-Corner. b) If the manager schedules 45 minutes of breaks for the 8-hour shift only 435 minutes are available for quilting time. Approximately what is the probability that the total amount of time needed to quilt the 33 tops of randomly selected quilt tops exceed the available 8-hour shift? Show your work! ...
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