Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Using the normal distribution and the central limit theorem, it is found that there is a 0.0409 = 4.09% probability that, from a simple random sample of 300 adults in the county, less than 50% would say they believe that gardening should be part of the school curriculum.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample proportions for a proportion p in a sample of size n has [tex]\mu = p, s = \sqrt{\frac{p(1 - p)}{n}}[/tex]
In this problem:
- The proportion is of 55%, hence [tex]p = 0.55[/tex]
- The sample has 300 adults, hence [tex]n = 300[/tex]
Then, the mean and the standard error are given by:
[tex]\mu = p = 0.55[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.55(0.45)}{300}} = 0.0287[/tex]
The probability is the p-value of Z when X = 0.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.55}{0.0287}[/tex]
[tex]Z = -1.74[/tex]
[tex]Z = -1.74[/tex] has a p-value of 0.0409.
0.0409 = 4.09% probability that, from a simple random sample of 300 adults in the county, less than 50% would say they believe that gardening should be part of the school curriculum.
A similar problem is given at https://brainly.com/question/25800303
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
