Stat-101 FL23 Project 1 Version 1 – Chapter 1, 2, 3 Name:____________________________________________ UIN: _____________________ Please write your full name as registered and so that it is easy to read. Please include your UIC ID Number (UIN). Also, please write in the space below as clearly as possible since several people may be grading your worksheets. Lastly, please take clear photos of each page to upload to Gradescope. Use the link in our Blackboard course to get there. If you want to use your own paper, please write the same number of problems per page and the same number of pages or a penalty may be applied. Academic honesty agreement, please only use your own thoughts and writing for this assignment. This is an individual project.
1. Assume that the length of time (in minutes) that you wait in line for a roller coaster ride is based on the Normal Distribution with a ???? = 45 minutes and ???? = 3 minutes.
a. Using the image below, label the standard deviations using the Empirical Rule (68-95-99.7). Label the x- axis with the data values for each standard deviation away from the mean and label the mean.
Using the information from the graph, answer the following questions.
b. 68% of the time, the wait time is between _______________ minutes and _____________ minutes
c. 99.7% of the time, the wait time is between _______________ minutes and _____________ minutes
d. What percentage of the time is the wait in line for roller coaster less than 42 minutes? ____________
e. What percentage of the time is the wait in line between 39 and 48 minutes? ____________
f. Sarah waited 47 minutes in line to ride the roller coaster. Compute the z-score for this wait time. Round to two decimal places and show work.
Stat-101 FL23 Project 1 – Chapter 1, 2, 3 Name:____________________________________________ UIN: _____________________
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2. For the next ride, Sarah waited 18 minutes in line for the bumper cars ride. The length of time (in minutes) you wait in line for the bumper cars is based on the Normal distribution with ???? = 22 minutes and ???? = 6 minutes.
a. Compute the z-score for Sarah’s wait time and round to two decimal places. Show work below.
b. Based on the z-score that you found, what does this tell you about Sarah’s wait time compared to the mean? Circle one option. It is shorter than average It is longer than average It is average
c. Based on your results for the wait times that Sarah experienced for the roller coaster ride and the bumper cars, which wait time was worse? Roller Coaster Bumper Cars They were the same
3. If we are given a Normal distribution with such at N(39, 4). Answer the following questions.
a. What is the mean of the distribution? __________________
b. What is the standard deviation of the distribution? ________________
c. If we know that a data value x has a z-score of 1.54, find the data value x. Do not round. Show work.
d. If we know that a data value x has a z-score of -0.83, find the data value x. Do not round. Show work.
Stat-101 FL23 Project 1 – Chapter 1, 2, 3 Name:____________________________________________ UIN: _____________________
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4. Assume that the average wait time at Starbucks drive thru is 4.4 minutes with a standard deviation of 0.3 minutes. If we assume that the distribution is Normally distributed, answer the following questions.
a. Using the Normal curve below, label the standard deviations with the related minutes. Included the mean.
b. Find the z-score for 3.75 minutes. Label this time on the chart above. Show work below.
c. What is the area under the curve that corresponds to waiting times of less than 3.75 minutes? Round to 4 decimal places if needed.
d. Convert your answer from part (C) to a percentage and write a sentence describing what this means.
e. What is the area under the curve that corresponds to waiting times of 3.75 minutes up to 5.3 minutes? Round to 4 decimal places.
Stat-101 FL23 Project 1 – Chapter 1, 2, 3 Name:____________________________________________ UIN: _____________________
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5. A description of different houses on the market includes the variables “square footage of the house” and “average monthly gas bill” and “construction materials.” Circle the correct option for the types of variables these are:
a. Square footage is categorical quantitative
b. Average monthly gas bill is categorical quantitative
c. Construction materials is categorical quantitative
6. What are the statistics needed to write a five-number summary? Write a complete sentence below.
7. If the histogram for a dataset is skewed right, what does that mean about the relationship between the mean and the median?
8. What percentage of the observations in a Normal distribution are greater than the first quartile? Write a complete sentence below.