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Ch. 6 - Normal Probability Distributions
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoTriola 14th EditionCh. 6 - Normal Probability DistributionsProblema 6.1.42
Capitolo 6, Problema 6.1.42

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


z0.90

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Step 1: Understand the problem. The critical value z0.90 represents the z-score that corresponds to a cumulative area of 0.90 under the standard normal distribution curve.
Step 2: Recall that the cumulative area under the standard normal curve to the left of a z-score is given by the standard normal distribution table or a statistical calculator.
Step 3: To find z0.90, locate the z-score where the cumulative probability (area to the left) is 0.90. This can be done using a z-table or statistical software.
Step 4: If using a z-table, find the closest cumulative probability to 0.90 in the table and identify the corresponding z-score. If using software, input the cumulative probability of 0.90 to obtain the z-score.
Step 5: Round the resulting z-score to two decimal places as specified in the problem.

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Critical Value

A critical value is a point on the scale of the test statistic beyond which we reject the null hypothesis. In the context of a normal distribution, it represents the z-score that corresponds to a specified level of significance or confidence level. For example, a critical value of z0.90 indicates the z-score that leaves 10% in the upper tail of the distribution.
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Critical Values: t-Distribution

Z-Score

A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated by subtracting the mean from the value and then dividing by the standard deviation. Z-scores are used in hypothesis testing and confidence intervals to determine how far away a data point is from the mean in terms of standard deviations.
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Z-Scores From Given Probability - TI-84 (CE) Calculator

Standard Normal Distribution

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is used as a reference for calculating probabilities and critical values. Any normal distribution can be transformed into a standard normal distribution using z-scores, allowing for easier comparison and analysis of different datasets.
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Finding Standard Normal Probabilities using z-Table
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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?

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Pulse Rates. In Exercises 13–24, use the data in the table below for pulse rates of adult males and females (based on Data Set 1 “Body Data” in Appendix B). Hint: Draw a graph in each case.


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For males, find P90 which is the pulse rate separating the bottom 90% from the top 10%.

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IQ Scores. In Exercises 5–8, find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test).

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Interpreting Normal Quantile Plots. In Exercises 5–8, examine the normal quantile plot and determine whether the sample data appear to be from a population with a normal distribution.


Ages of Presidents The normal quantile plot represents the ages of presidents of the United States at the times of their inaugurations. The data are from Data Set 22 “Presidents” in Appendix B.

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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?

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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

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