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.
Between z=0 and z=2.86
84
views
Ch. 5 - Normal Probability Distributions
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 5.4.24
Interpreting the Central Limit Theorem In Exercises 19–26, find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution.
Salaries The annual salaries for web software development managers are normally distributed, with a mean of about \$136,000 and a standard deviation of about \$11,500. Random samples of 40 are drawn from this population, and the mean of each sample is determined.
Guida verificata passo dopo passo1
Identify the population mean (\$\(\mu\)\$) and population standard deviation (\$\(\sigma\)\$). Here, \$\(\mu\) = 136,000\$ and \$\(\sigma\) = 11,500\$.
Note the sample size \$n = 40\$ and recognize that the sampling distribution of the sample mean will have its own mean and standard deviation.
Calculate the mean of the sampling distribution of the sample mean, which is the same as the population mean: \$\(\mu\)_{\(\bar{x}\)} = \(\mu\) = 136,000\$.
Calculate the standard deviation of the sampling distribution of the sample mean (also called the standard error) using the formula: \$\(\sigma\)_{\(\bar{x}\)} = \(\frac{\sigma}{\sqrt{n}\)} = \(\frac{11,500}{\sqrt{40}\)}\$.
Since the population distribution is normal, the sampling distribution of the sample mean will also be normal. Sketch a normal curve centered at \$136,000\$ with spread determined by \$\(\sigma\)_{\(\bar{x}\)}\$.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Central Limit Theorem (CLT)
The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size becomes large, regardless of the population's distribution. For sample sizes typically greater than 30, the sample means will be approximately normally distributed, enabling inference about the population mean.
Video consigliato:
Percorso guidato
05:14
Central Limit Theorem
Sampling Distribution of the Sample Mean
The sampling distribution of the sample mean is the probability distribution of all possible sample means from samples of a fixed size. It has a mean equal to the population mean and a standard deviation (standard error) equal to the population standard deviation divided by the square root of the sample size.
Video consigliato:
Percorso guidato
06:53Sampling Distribution of Sample Mean
Standard Error of the Mean
The standard error measures the variability of the sample mean from the population mean. It is calculated as the population standard deviation divided by the square root of the sample size, reflecting how much sample means fluctuate around the true mean in repeated sampling.
Video consigliato:
Percorso guidato
04:52Calculating the Mean
Pratica correlata
Domanda del libro di testo
Graphical Analysis In Exercises 17–22, find the indicated z-score(s) shown in the graph.
" style="" width="260">
118
views
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=36, find the probability of a sample mean being less than 12,750 or greater than 12,753 when mu=12750 and 1.7.
105
views
Domanda del libro di testo
Computing and Interpreting z-Scores In Exercises 39 and 40, (a) find the z-score that corresponds to each value and (b) determine whether any of the values are unusual.
Stanford-Binet IQ Scores The test scores for the Stanford-Binet Intelligence Scale are normally distributed with a mean score of 100 and a standard deviation of 16. The test scores of four students selected at random are 98, 65, 106, and 124.
155
views
Domanda del libro di testo
Computing Probabilities for Normal Distributions In Exercises 1–6, the random variable x is normally distributed with mean mu=174 and standard deviation sigma=20. Find the indicated probability.
P(172 < x <192)
132
views
Domanda del libro di testo
Finding Probability In Exercises 47–56, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.
P(- 1.54 < z < 1.54)
92
views