Work in teams of three or four (person A, person B, and person C). Each student is to complete his or her worksheet using the me
thod as prescribed on the sheet, showing all work for each problem. When you are finished, compare solutions for each corresponding system. Write the agreed upon
solution in the appropriate column. Then discuss how Vou arrived at your solution. Was the method
you used easier or more difficult than the others? Decide which method or methods the group found
to be the 'best' or 'preferred' for each system (graphing, substitution or elimination). Give a reaso
for your answer. Simply saying, "it was the easiest method" is not sufficient. Explain WHY you found
the method to be the best-what made it easier?
solution in the appropriate column. Then discuss how Vou arrived at your solution. Was the method
you used easier or more difficult than the others? Decide which method or methods the group found
to be the 'best' or 'preferred' for each system (graphing, substitution or elimination). Give a reaso
for your answer. Simply saying, "it was the easiest method" is not sufficient. Explain WHY you found
the method to be the best-what made it easier?
1 answer:
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Answer:
a) 0.2741 = 27.41% probability that at least 13 believe global warming is occurring
b) 0.7611 = 76.11% probability that at least 110 believe global warming is occurring
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples 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 ,
.
In this problem, we have that:
(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring?
Here , we want
. So
In which
0.2741 = 27.41% probability that at least 13 believe global warming is occurring
(b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring?
Now . So
Using continuity correction, this is , which is 1 subtracted by the pvalue of Z when X = 109.5. So
has a pvalue of 0.2389
1 - 0.2389 = 0.7611
0.7611 = 76.11% probability that at least 110 believe global warming is occurring