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Ch. 6 - Normal Probability Distributions
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 6 - Normal Probability DistributionsProblem 6.c.1d
Chapter 6, Problem 6.c.1d

In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).


35 35 20 50 95 75 45 50 30 35 30 30


d. Find the variance.

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1
Step 1: Calculate the mean (average) of the data set. The formula for the mean is: μ = ∑xin, where n is the number of data points and ∑xi is the sum of all data points.
Step 2: Subtract the mean from each data point to find the deviation of each data point from the mean. This is calculated as: xi - μ for each data point.
Step 3: Square each deviation to eliminate negative values. This is calculated as: (xi - μ)2 for each data point.
Step 4: Find the average of the squared deviations. This is the variance, and the formula is: σ2 = ∑(xi - μ)2n, where n is the number of data points.
Step 5: Plug in the values from the data set into the formula and compute the variance. Ensure all calculations are accurate and double-check your work.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Variance

Variance is a statistical measure that represents the degree of spread or dispersion of a set of data points around their mean. It quantifies how much the individual data points differ from the average value. A higher variance indicates that the data points are more spread out, while a lower variance suggests they are closer to the mean. Variance is calculated by taking the average of the squared differences from the mean.
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Mean

The mean, often referred to as the average, is a measure of central tendency that is calculated by summing all the values in a data set and dividing by the number of values. It provides a single value that represents the center of the data distribution. Understanding the mean is essential for calculating variance, as it serves as the reference point from which deviations are measured.
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Data Set

A data set is a collection of related values or observations that can be analyzed statistically. In this context, the data set consists of wait times for a specific ride, which can be used to calculate various statistical measures, including variance. Understanding the structure and characteristics of the data set is crucial for accurate analysis and interpretation of results.
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Related Practice
Textbook Question

In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).


35 35 20 50 95 75 45 50 30 35 30 30


Tower of Terror Wait Times


a. Find Q1, Q2 and Q3.

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Textbook Question

Continuity Correction In testing the assumption that the probability of a baby boy is 0.512, a geneticist obtains a random sample of 1000 births and finds that 502 of them are boys. Using the continuity correction, describe the area under the graph of a normal distribution corresponding to the following. (For example, the area corresponding to “the probability of at least 502 boys” is this: the area to the right of 501.5.)


c. The probability of more than 502 boys

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Textbook Question

In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).


35 35 20 50 95 75 45 50 30 35 30 30


g. What level of measurement (nominal, ordinal, interval, ratio) describes this data set?

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Textbook Question

Significance For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are


c. not significant (or less than 2 standard deviations away from the mean).

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Textbook Question

Sleepwalking Assume that 29.2% of people have sleepwalked (based on “Prevalence and Comorbidity of Nocturnal Wandering in the U.S. Adult General Population, by Ohayon et al., Neurology, Vol. 78, No. 20). Assume that in a random sample of 1480 adults, 455 have sleepwalked.


c. What does the result suggest about the rate of 29.2%?

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Textbook Question

Ergonomics. Exercises 9–16 involve applications to ergonomics, as described in the Chapter Problem.


Safe Loading of Elevators The elevator in the car rental building at San Francisco International Airport has a placard stating that the maximum capacity is “4000 lb—27 passengers.” Because 4000/27=148, this converts to a mean passenger weight of 148 lb when the elevator is full. We will assume a worst-case scenario in which the elevator is filled with 27 adult males. Based on Data Set 1 “Body Data” in Appendix B, assume that adult males have weights that are normally distributed with a mean of 189 lb and a standard deviation of 39 lb.


c. What do you conclude about the safety of this elevator?

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