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molliemoo1002
20.04.2021 •
Mathematics
Which shows the following percent written as both a decimal and a fraction?
1/2 %
0.05 ; 1/20 0.005 ; 1/200 0.5 ; 1/2 0.5 1/200
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Ответ:
0.9983 = 99.83% probability that a majority will favor the proposal.
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed distributions can be 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.
When we are approximating a binomial distribution to a normal one, we have that
,
.
Suppose that 70% of the faculty favor the pass/fail proposal. Assuming 50 faculty members are interviewed.
This means, respectively, that![p = 0.7, n = 50](/tpl/images/1138/6480/7c080.png)
Mean and standard deviation:
Probability that a majority (26 or more) will favor the proposal.
Using continuity correction, this is
, which is 1 subtracted by the pvalue of Z when X = 25.5. So
1 - 0.0017 = 0.9983
0.9983 = 99.83% probability that a majority will favor the proposal.