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Using the normal approximation to the binomial, it is found that:
- The mean of X is of 52 samples.
- The standard deviation of X is of 4.2661 samples.
- 0.0017 = 0.17% probability that less than half without any traces of pesticide.
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Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, with mean given by:
And standard deviation of:
Normal probability distribution
Z-score formula is used, which, in a set with mean and standard deviation
, the z-score of a measure X is given by:
- Each z-score has an associated p-value, which measures the percentile of measure X.
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- 65% of samples had no pesticide, thus
- 80 samples, thus
The mean of X is of:
The standard deviation of X is of:
Using the approximation and continuity correction, the probability is , which is the p-value of Z when X = 39.5. Thus:
has a p-value of 0.0017, thus:
0.0017 = 0.17% probability that less than half without any traces of pesticide.
A similar problem is given at brainly.com/question/24261244