The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find
1 answer:
Answer:
The probability of getting someone who tests positive, given that he or she had the disease is 0.8954.
Step-by-step explanation:
The data provided is:
YES NO Total
Positive 137 8 145
Negative 16 139 155
Total 153 147 300
An individual is selected at random from the group.
We need to compute the probability of getting someone who tests positive, given that he or she had the disease.
The conditional probability of an event <em>A</em> given that another event <em>B</em> has already occurred is:
Let <em>A</em> = individuals who tests positive and <em>B</em> = individual who had the disease.
The number of individuals who tests positive and had the disease is,
n (A ∩ B) = 137
n (B) = 153
Compute the conditional probability of A given B as follows:
Thus, the probability of getting someone who tests positive, given that he or she had the disease is 0.8954.
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Answer:
The difference of 8 times a number r and 12 is solved for a number r and is given by
Step-by-step explanation:
Given problem is the difference of 8 times a number r and 12
It can be written as
To simplify the above expression :
8r-12
( using addition property of equality )
(using division property of equality )
Therefore
Therefore the difference of 8 times a number r and 12 is solved for a number r and is given by
Answer:
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly
This probability is the pvalue of Z when X = 1600 + 300 = 1900 subtracted by the pvalue of Z when X = 1600 - 300 = 1300. So
X = 1900
By the Central Limit Theorem
has a pvalue of 0.9535.
X = 1300
has a pvalue of 0.0465.
0.9535 - 0.0465 = 0.907.
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.