541,000 to the nearest ten thousand
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Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0.0166 = 1.66% probability of a sample proportion of 0.59 or less.
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 sampling proportions of a proportion p in a sample of size n has mean
and standard error
In this problem:
- 1,190 adults were asked, hence
- In fact 62% of all adults favor balancing the budget over cutting taxes, hence
.
The mean and the standard error are given by:
The probability of a sample proportion of 0.59 or less is the <u>p-value of Z when X = 0.59</u>, hence:
By the Central Limit Theorem
has a p-value of 0.0166.
0.0166 = 1.66% probability of a sample proportion of 0.59 or less.
You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213