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=0.33
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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 5.4.41
Construction About 63% of the residents in a town are in favor of building a new high school. One hundred five residents are randomly selected. What is the probability that the sample proportion in favor of building a new school is less than 55%? Interpret your result.
Guida verificata passo dopo passo1
Step 1: Identify the given information. The population proportion (p) is 0.63, the sample size (n) is 105, and we are interested in the probability that the sample proportion (p̂) is less than 0.55.
Step 2: Calculate the mean (μ) and standard deviation (σ) of the sampling distribution of the sample proportion. The mean is equal to the population proportion, μ = p = 0.63. The standard deviation is calculated using the formula: σ = sqrt((p * (1 - p)) / n).
Step 3: Standardize the sample proportion to find the z-score. Use the formula: z = (p̂ - μ) / σ, where p̂ is the sample proportion (0.55 in this case). Substitute the values of μ and σ from the previous step.
Step 4: Use the z-score to find the cumulative probability. Look up the z-score in the standard normal distribution table or use statistical software to find the probability that corresponds to the z-score.
Step 5: Interpret the result. The cumulative probability represents the likelihood that the sample proportion is less than 55%. This value can be interpreted in the context of the problem to understand how unusual it is for the sample proportion to be below 55% given the population proportion of 63%.
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Sample Proportion
The sample proportion is the ratio of the number of individuals in a sample who exhibit a certain characteristic to the total number of individuals in that sample. In this context, it refers to the proportion of residents in favor of building a new high school among the 105 randomly selected residents. Understanding sample proportion is crucial for estimating population parameters and conducting hypothesis tests.
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Percorso guidato
05:11
Sampling Distribution of Sample Proportion
Normal Approximation to the Binomial Distribution
When dealing with proportions, especially in large samples, the sampling distribution of the sample proportion can be approximated by a normal distribution due to the Central Limit Theorem. This approximation is valid when both np and n(1-p) are greater than 5, where n is the sample size and p is the population proportion. This concept allows us to calculate probabilities related to sample proportions using the properties of the normal distribution.
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Percorso guidato
06:23Using the Normal Distribution to Approximate Binomial Probabilities
Probability Interpretation
Probability interpretation involves understanding the likelihood of an event occurring within a given context. In this question, it requires interpreting the calculated probability that the sample proportion of residents in favor of the new school is less than 55%. This interpretation helps in making informed decisions based on statistical evidence and understanding the implications of the results in the context of community support for the school.
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Percorso guidato
5:37Introduction to Probability
Pratica correlata
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 = 150, sigma =25, n = 49
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Domanda del libro di testo
Graphical Analysis In Exercises 9 and 10, the graph of a population distribution is shown with its mean and standard deviation. Random samples of size 100 are drawn from the population. Determine which of the figures labeled (a)–(c) would most closely resemble the sampling distribution of sample means. Explain your reasoning.
The waiting time (in seconds) to turn left at an intersection
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Domanda del libro di testo
Graphical Analysis In Exercises 17–22, find the indicated z-score(s) shown in the graph.
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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.
P91
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Domanda del libro di testo
True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
As the sample size increases, the mean of the distribution of sample means increases.
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