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= -1.55 and z= 1.55
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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 5.4.3
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 = 790, sigma =48, n = 250
Guida verificata passo dopo passo1
Step 1: Recall the formula for the mean of the sampling distribution of sample means. The mean of the sampling distribution (denoted as μₓ̄) is equal to the population mean (μ). Therefore, μₓ̄ = μ.
Step 2: Substitute the given value of the population mean (μ = 790) into the formula. This means the mean of the sampling distribution is μₓ̄ = 790.
Step 3: Recall the formula for the standard deviation of the sampling distribution of sample means, also known as the standard error (SE). The formula is SE = σ / √n, where σ is the population standard deviation and n is the sample size.
Step 4: Substitute the given values into the formula for SE. Here, σ = 48 and n = 250. The formula becomes SE = 48 / √250.
Step 5: Simplify the expression for SE by calculating the square root of 250 and dividing 48 by that value. This will give you the standard deviation of the sampling distribution of sample means.
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Sampling Distribution
The sampling distribution of the sample mean is the probability distribution of all possible sample means from a population. It describes how the means of different samples will vary and is crucial for understanding the behavior of sample statistics. According to the Central Limit Theorem, as the sample size increases, the sampling distribution approaches a normal distribution, regardless of the population's distribution.
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Sampling Distribution of Sample Proportion
Mean of the Sampling Distribution
The mean of the sampling distribution of sample means, also known as the expected value, is equal to the population mean (mu). This means that if you take many samples and calculate their means, the average of those means will converge to the population mean. In this case, with mu = 790, the mean of the sampling distribution will also be 790.
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05:11Sampling Distribution of Sample Proportion
Standard Deviation of the Sampling Distribution
The standard deviation of the sampling distribution, known as the standard error, measures the variability of sample means around the population mean. It is calculated by dividing the population standard deviation (sigma) by the square root of the sample size (n). For this problem, with sigma = 48 and n = 250, the standard error can be computed to understand how much sample means will typically deviate from the population mean.
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05:11Sampling Distribution of Sample Proportion
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