Domanda del libro di testo
Given the mean of a normal distribution, how can you find the median?
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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 5.4.17
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.
Guida verificata passo dopo passo1
Step 1: Identify the given values in the problem. The population mean (μ) is 550, the population standard deviation (σ) is 3.7, the sample size (n) is 45, and we are tasked with finding the probability of the sample mean (x̄) being greater than 551.
Step 2: Calculate the standard error of the mean (SE). The formula for the standard error is: . Substitute the values: .
Step 3: Compute the z-score for the sample mean. The formula for the z-score is: . Substitute the values: .
Step 4: Use the z-score to find the probability. Look up the z-score in the standard normal distribution table or use statistical software to find the cumulative probability. Since the problem asks for the probability of the sample mean being greater than 551, calculate .
Step 5: Determine if the sample mean is unusual. A sample mean is considered unusual if the probability is less than 0.05 (5%). Compare the calculated probability to this threshold to make the determination.
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Central Limit Theorem
The Central Limit Theorem states that the distribution of sample means will approach a normal distribution as the sample size increases, regardless of the population's distribution, provided the sample size is sufficiently large (typically n > 30). This theorem is crucial for calculating probabilities related to sample means.
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Percorso guidato
04:52
Calculating the Mean
Standard Error
Standard Error (SE) measures the dispersion of sample means around the population mean. It is calculated as the population standard deviation divided by the square root of the sample size (SE = sigma / √n). In this case, it helps determine how much variability to expect in the sample mean.
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08:45Calculating Standard Deviation
Z-Score
A Z-score indicates how many standard deviations an element is from the mean. It is calculated using the formula Z = (X - mu) / SE, where X is the sample mean. This score is essential for finding probabilities in a standard normal distribution and determining if a sample mean is unusual.
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06:31Z-Scores From Given Probability - TI-84 (CE) Calculator
Pratica correlata
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.
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Domanda del libro di testo
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.
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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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