Domanda del libro di testo
Finding Area In Exercises 23–36, find the indicated area under the standard normal curve. If convenient, use technology to find the area.
To the left of z= -1.28 and to the right of z= 1.28
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Ch. 5 - Normal Probability Distributions
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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TOC.tableOfContents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Capitolo 5, Problema 5.1.51
Finding Probability In Exercises 47–56, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.
P(- 0.89 < z < 0)
Guida verificata passo dopo passo1
Step 1: Understand the problem. The goal is to find the probability that the standard normal variable z falls between -0.89 and 0. This involves using the standard normal distribution, which has a mean of 0 and a standard deviation of 1.
Step 2: Recall that the standard normal distribution table (or z-table) provides the cumulative probability from the far left of the distribution up to a given z-value. Alternatively, technology such as a graphing calculator or statistical software can be used to find probabilities.
Step 3: Break the problem into two parts. First, find the cumulative probability for z = 0. From the properties of the standard normal distribution, the cumulative probability for z = 0 is 0.5 (since it is the mean of the distribution).
Step 4: Next, find the cumulative probability for z = -0.89. Use a z-table or technology to determine this value. The z-table will give the cumulative probability from the far left of the distribution up to z = -0.89.
Step 5: Subtract the cumulative probability for z = -0.89 from the cumulative probability for z = 0. This difference represents the probability that z falls between -0.89 and 0. Mathematically, this is expressed as P(-0.89 < z < 0) = P(z < 0) - P(z < -0.89).
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Standard Normal Distribution
The standard normal distribution is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. It is represented by the variable 'z', which indicates how many standard deviations an element is from the mean. This distribution is crucial for calculating probabilities and is often used in statistical analysis to standardize scores.
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Percorso guidato
09:47
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 allow for the comparison of scores from different distributions and are essential for finding probabilities in the standard normal distribution.
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06:31Z-Scores From Given Probability - TI-84 (CE) Calculator
Probability Calculation
Probability calculation in the context of the standard normal distribution involves finding the area under the curve between two z-scores. This area represents the likelihood of a value falling within that range. Tools such as z-tables or statistical software can be used to determine these probabilities, making it easier to analyze data and draw conclusions.
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07:09Probability From Given Z-Scores - TI-84 (CE) Calculator
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