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 5.3.3
Finding a z-Score In Exercises 1–16, use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area or percentile.
0.6736
Guida verificata passo dopo passo1
Step 1: Understand the problem. The goal is to find the z-score that corresponds to a cumulative area (or percentile) of 0.6736 under the standard normal distribution curve. The cumulative area represents the probability that a value is less than or equal to the z-score.
Step 2: Recall the properties of the standard normal distribution. The standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1. The cumulative area is the area under the curve to the left of the z-score.
Step 3: Use the Standard Normal Table (also called the z-table) or technology. Locate the cumulative area of 0.6736 in the table. The table provides the cumulative area for various z-scores. Alternatively, use statistical software or a calculator with a built-in function to find the z-score corresponding to this cumulative area.
Step 4: Match the cumulative area to the closest value in the z-table. Identify the row and column that correspond to this cumulative area. The intersection of the row and column gives the z-score. If using technology, input the cumulative area (0.6736) into the appropriate function to directly obtain the z-score.
Step 5: Interpret the result. The z-score represents the number of standard deviations the value is from the mean. A positive z-score indicates the value is above the mean, while a negative z-score indicates it is below the mean.
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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 indicates how many standard deviations an element is from the mean. A positive z-score means the value is above the mean, while a negative z-score indicates it is below. Z-scores are essential for standardizing scores on different scales, allowing for comparison across different datasets.
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Percorso guidato
06:31
Z-Scores From Given Probability - TI-84 (CE) Calculator
Standard Normal Distribution
The standard normal distribution is a special case of the normal distribution where the mean is 0 and the standard deviation is 1. It is symmetrical and bell-shaped, representing the distribution of many natural phenomena. The area under the curve corresponds to probabilities, and z-scores can be used to find the cumulative area to the left of a given value, which is crucial for interpreting statistical data.
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09:47Finding Standard Normal Probabilities using z-Table
Cumulative Area
Cumulative area refers to the total area under the curve of a probability distribution up to a certain point. In the context of the standard normal distribution, it represents the probability that a randomly selected score will be less than or equal to a specific z-score. This concept is vital for determining percentiles and understanding how data is distributed relative to the mean.
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03:50Probabilities Between Two Values
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Domanda del libro di testo
Finding Probabilities In Exercises 15–18, the population mean and standard deviation are given. Find the indicated probability and determine whether the given sample mean would be considered unusual.
For a random sample of n=64, find the probability of a sample mean being less than 24.3 when Mu=24 and sigma=1.25.
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Domanda del libro di testo
Which Is More Likely? Assume that the fertility rates in Exercise 32 are normally distributed. Are you more likely to randomly select a state with a fertility rate of less than 65 or to randomly select a sample of 15 states in which the mean of the state fertility rates is less than 65? Explain.
65
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Domanda del libro di testo
Finding Probabilities In Exercises 15–18, the population mean and standard deviation are given. Find the indicated probability and determine whether the given sample mean would be considered unusual.
For a random sample of n=45, find the probability of a sample mean being greater than 551 when mu=550 and sigma=3.7.
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Domanda del libro di testo
Using and Interpreting Concepts
Finding Area In Exercises 17–22, find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area.
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Domanda del libro di testo
In Exercises 1–4, a population has a mean mu and a standard deviation sigma. Find the mean and standard deviation of the sampling distribution of sample means with sample size n.
Mu = 45, sigma =15, n = 100
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