Stat 101 Fl23 Project 1, Chapter 1–3

Stat 101 Fl23 Project 1 Version 1 Chapter 1 2 3

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 μ = 45 minutes and σ = 3 minutes. a. Using the image below, label the standard deviations using the Empirical Rule. 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.

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 μ = 22 minutes and σ= 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.

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. Show work. d. If we know that a data value x has a z-score of -0.83, find the data value x. Show work.

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. Include the mean. b. Find the z-score for 3.75 minutes. 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.

A description of different houses on the market includes the variables “square footage of the house,” “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.

What are the statistics needed to write a five-number summary? Write a complete sentence below.

If the histogram for a dataset is skewed right, what does that mean about the relationship between the mean and the median? Write a complete sentence below.

What percentage of the observations in a Normal distribution are greater than the first quartile? Write a complete sentence below.

Paper For Above instruction

The assignment requires detailed statistical analysis based on normal distributions and variables applicable to real-world data and scenarios. The first task involves illustrating the empirical rule on a normal distribution of roller coaster wait times, specifically labeling standard deviations on a graph, and describing the percentage of data within certain ranges. Calculating the percentage of wait times less than a specific value and between two values demonstrates understanding of the empirical rule and z-scores. For Sarah’s wait times, the task involves computing z-scores, interpreting these scores, and comparing the wait times to determine which was worse.

The next section assesses understanding of normal distribution parameters. Given a normally distributed dataset, you’ll compute the mean and standard deviation, and use z-scores to find corresponding data values. This demonstrates proficiency in standardizing data points and reversibility of the z-score transformation.

Further, the assignment examines real-world application through Starbucks drive-thru wait times, asking to label standard deviations on a normal curve, compute z-scores, and interpret the probabilities associated with specific wait times. These calculations are essential for understanding customer experience metrics and process improvements.

Additional questions delve into the nature of variables in real estate data, asking to classify variables as categorical or quantitative, emphasizing understanding of variable types and their implications for analysis. The task of describing a five-number summary requires articulating the components (minimum, Q1, median, Q3, maximum), crucial for describing data distributions.

Finally, the assignment addresses the implications of skewness in histograms, specifically right skewness, which indicates the mean is greater than the median. It also queries understanding of what proportion of data in a normal distribution exceeds the first quartile, linking concepts of quartiles and probabilities in a normally distributed dataset.

References

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