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Using the <u>normal distribution and the central limit theorem</u>, 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 and standard deviation
, the z-score of a measure X is given by:
- 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
In this problem:
- The proportion is of 55%, hence
- The sample has 300 adults, hence
Then, the <u>mean and the standard error</u> are given by:
The probability is the <u>p-value of Z when X = 0.5,</u> hence:
By the Central Limit Theorem
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 brainly.com/question/25800303