pimuang50
04.03.2020 •
Mathematics
It’s estimated that 52% of American adults have incurred credit card debt. The department of finance surveys 2500 adults for a report.
Determine the probability that between 1200 and 1450 of those surveyed incurred debt.
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Ответ:
100% probability that between 1200 and 1450 of those surveyed incurred debt.
Step-by-step explanation:
We use the binomial approximation to the normal 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 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:
So
Determine the probability that between 1200 and 1450 of those surveyed incurred debt.
This is the pvalue of Z when X = 1450 subtracted by the pvalue of Z when X = 1200. So
X = 1450
has a pvalue of 1
X = 1200
has a pvalue of 0
1 - 0 = 1
100% probability that between 1200 and 1450 of those surveyed incurred debt.
Ответ:
1\4z-5\8x=-7
Step-by-step explanation:
collect like terms together