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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 6.1.42
Chapter 6, Problem 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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Key Concepts

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

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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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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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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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?

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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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Textbook Question

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