Ch. 6 - Normal Probability Distributions

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 6 - Normal Probability Distributions

Problem 6.5.12

Chapter 6, Problem 6.5.12

Determining Normality. In Exercises 9–12, refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is roughly bell-shaped.

Dunkin’ Donuts The drive-through service times (seconds) of Dunkin’ Donuts lunch customers, as listed in Data Set 36 “Fast Food” in Appendix B

Verified step by step guidance

Step 1: Organize the data. Begin by listing the drive-through service times provided in the data set. Ensure the data is sorted in ascending order to make further analysis easier.

Step 2: Create a histogram. Divide the range of the data into intervals (bins) and plot the frequency of data points in each bin. A roughly bell-shaped histogram suggests normality.

Step 3: Construct a normal probability plot (Q-Q plot). Plot the quantiles of the sample data against the quantiles of a standard normal distribution. If the points form a straight line, the data is approximately normal.

Step 4: Calculate summary statistics. Compute the mean, median, and standard deviation of the data. For a normal distribution, the mean and median should be close, and the data should be symmetric around the mean.

Step 5: Perform a formal test for normality. Use statistical tests such as the Shapiro-Wilk test or Anderson-Darling test to assess whether the data comes from a normal distribution. Compare the p-value to the significance level (e.g., 0.05) to make a conclusion.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Normal Distribution

Normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. It is often represented as a bell-shaped curve, where the mean, median, and mode are all equal. Understanding this concept is crucial for determining if a dataset approximates a normal distribution.

Central Limit Theorem

The Central Limit Theorem states that the sampling distribution of the sample mean will tend to be normally distributed, regardless of the shape of the population distribution, as the sample size becomes large. This theorem is fundamental in statistics because it allows for the use of normal distribution techniques even when the original data is not normally distributed, provided the sample size is sufficiently large.

Normality Tests

Normality tests are statistical tests used to determine if a dataset follows a normal distribution. Common tests include the Shapiro-Wilk test and the Kolmogorov-Smirnov test. These tests provide a formal method to assess normality, which is essential for validating assumptions in various statistical analyses, particularly those that rely on normality.

Recommended video:

Guided course

06:34

Step 2: Calculate Test Statistic

Related Practice

Textbook Question

Good Sample? An economist is investigating the incomes of college students. Because she lives in Maine, she obtains sample data from that state. Is the resulting mean income of college students a good estimator of the mean income of college students in the United States? Why or why not?

111

views

Textbook Question

Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places.

z0.90

230

views

Textbook Question

Overbooking a Boeing 767-300 A Boeing 767-300 aircraft has 213 seats. When someone buys a ticket for a flight, there is a 0.0995 probability that the person will not show up for the flight (based on data from an IBM research paper by Lawrence, Hong, and Cherrier). How many reservations could be accepted for a Boeing 767-300 for there to be at least a 0.95 probability that all reservation holders who show will be accommodated?

182

views

Textbook Question

Notation Common tests such as the SAT, ACT, LSAT, and MCAT tests use multiple choice test questions, each with possible answers of a, b, c, d, e, and each question has only one correct answer. For people who make random guesses for answers to a block of 100 questions, identify the values of p, q, μ, and σ. What do μ and σ measure?

173

views

Textbook Question

Continuous Uniform Distribution. In Exercises 5–8, refer to the continuous uniform distribution depicted in Figure 6-2 and described in Example 1. Assume that a passenger is randomly selected, and find the probability that the waiting time is within the given range.

Between 2 minutes and 3 minutes

167

views

Textbook Question

Hypothesis Testing. In Exercises 17–19, apply the central limit theorem to test the given claim. (Hint: See Example 3.)

Adult Sleep Times (hours) of sleep for randomly selected adult subjects included in the National Health and Nutrition Examination Study are listed below. Here are the statistics for this sample: n = 12, x_bar = 6.8 hours, s = 20 hours. The times appear to be from a normally distributed population. A common recommendation is that adults should sleep between 7 hours and 9 hours each night. Assuming that the mean sleep time is 7 hours, find the probability of getting a sample of 12 adults with a mean of 6.8 hours or less. What does the result suggest about a claim that “the mean sleep time is less than 7 hours”?

4 8 4 4 8 6 9 7 7 10 7 8

169

views