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kendallreed39
04.04.2020 •
Mathematics
Just before a referendum on a school budget, a local newspaper polls 354 voters to predict whether the budget will pass. Suppose the budget has the support of 55% of the voters. What is the probability that the newspaper's sample will lead it to predict defeat?
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Ответ:
3.07% probability that the newspaper's sample will lead it to predict defeat
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For a proportion p with n voters, we use![\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}}](/tpl/images/0582/3960/8a460.png)
In this problem, we have that:
So
What is the probability that the newspaper's sample will lead it to predict defeat?
That is, a percentage of 50% or less, which is the pvalue of Z when X = 0.5. So
3.07% probability that the newspaper's sample will lead it to predict defeat
Ответ: