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Ch. 5 - Normal Probability Distributions
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 5 - Normal Probability DistributionsProblema 5.RE.14
Capitolo 5, Problema 5.RE.14

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.


Between z = -1.55 and z = 1.04

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Step 1: Understand the problem. You are tasked with finding the area under the standard normal curve between z = -1.55 and z = 1.04. The standard normal curve is symmetric and has a mean of 0 and a standard deviation of 1.
Step 2: Recall that the area under the standard normal curve corresponds to probabilities. To find the area between two z-scores, you need to calculate the cumulative probability for each z-score using the standard normal distribution table or technology.
Step 3: Use the cumulative distribution function (CDF) for the standard normal distribution to find the cumulative probability for z = -1.55. This gives the area to the left of z = -1.55.
Step 4: Similarly, use the CDF to find the cumulative probability for z = 1.04. This gives the area to the left of z = 1.04.
Step 5: Subtract the cumulative probability for z = -1.55 from the cumulative probability for z = 1.04. This difference represents the area under the curve between z = -1.55 and z = 1.04.

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Standard Normal Distribution

The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation of 1. It is represented by the z-score, which indicates how many standard deviations an element is from the mean. This distribution is crucial for calculating probabilities and areas under the curve, as it allows for the standardization of different normal distributions.
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Finding Standard Normal Probabilities using z-Table

Z-scores

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 essential for determining the area under the standard normal curve, as they allow us to find probabilities associated with specific values.
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Z-Scores From Given Probability - TI-84 (CE) Calculator

Area Under the Curve

The area under the curve in a standard normal distribution represents the probability of a random variable falling within a certain range. To find the area between two z-scores, one can use statistical tables or technology, such as calculators or software, which provide cumulative probabilities. This area is critical for understanding the likelihood of outcomes in statistics.
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