Question

In: Statistics and Probability

In a certain risk group, individuals are tested for a certain disease S. A person who...

In a certain risk group, individuals are tested for a certain disease S. A person who has the disease gets the correct diagnosis with probability 0.99, whereas a person who does not suffer from S gets the correct diagnosis with probability 0.95. Furthermore, it is known that 6% of the individuals in the group get the diagnosis “suffer from S”. Determine a) the proportion of individuals in the group who suffer from S, and b) the probability that a person who gets the diagnosis “suffer from S” carries the disease.

Expert Solution

Answer:-

Given That:-

In a certain risk group, individuals are tested for a certain disease S. A person who has the disease gets the correct diagnosis with probability 0.99, whereas a person who does not suffer from S gets the correct diagnosis with probability 0.95. Furthermore, it is known that 6% of the individuals in the group get the diagnosis “suffer from S”. Determine a) the proportion of individuals in the group who suffer from S, and b) the probability that a person who gets the diagnosis “suffer from S” carries the disease.

(1) The probability that a person gets the diagnosis "Suffer from fever " actually carries the disease is 0.95

(2) The probability that a randomly selected person has fever or correct doagnosis is 0.061

Step-by - step explanation:

Denote the events as follows:

X = a person carries the disease

Y=the diagnosis is correct .

The information probvided is :

(1) The conditional probability of an event B given that another event A has already occurred is:

Use the conditional probability rule to determine the value of the asked probability

The probability that a person gets the diagnosis "suffer from fever " actual carries the disease can be expressed as follows :

The law of total probability states that:

Compute the probability of event X using the law of total probability as follows:

The value of P(X\Y) is:

Thus, the probability that a person gets the diagnosis "Suffer from fever" actually carries the disease is 0.96

orchestra answered 2 years ago

What population(s) is/are at highest risk of contracting the disease? Are there any groups of people who should be tested?

answer this about Chagas Disease Population(s) affected: What population(s) is/are at highest risk of contracting the disease? Are there any groups of people who should be tested? Please include statistical/geographical data and trends (from the Centers for Disease Control and Prevention, World Health Organization, or other source [http://www.cdc.gov, http://www.who.int, etc.]).

1. The percentage of tested patients with disease who actually tested positive is called: a. Specificity...

1. The percentage of tested patients with disease who actually tested positive is called: a. Specificity b. Negative predictive value c. Sensitivity d. Positive predictive value 2. The percentage of patients with a negative test who actually do NOT have the disease is called: a. Negative predictive value b. Sensitivity c. Specificity d. Positive predictive value 3. The percentage of tested patients without disease who actually tested negative is called: a. Negative predictive value b. Specificity c. Sensitivity d. Positive...

A diagnostic test for a certain disease is applied to n individuals known to not have...

A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive indicating presence of the disease, so X is the number of false positives) and p = the probability that a disease-free individual's test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than...

For a certain group of individuals, the average cost of a trip to the Super Bowl...

For a certain group of individuals, the average cost of a trip to the Super Bowl was $75. The standard deviation of the population was $50. This year, 49 fans who scheduled the trip paid an average of $89 for the three-day trip. Test the claim that the average cost is greater than last year’s cost at 1% significance level?

The prevalence of a disease is the fraction of individuals who are afflicted, i.e., the ratio...

The prevalence of a disease is the fraction of individuals who are afflicted, i.e., the ratio of the number of cases to the whole population. The incidence of a disease is the fraction of individuals who become infected in one time period, usually one year. This terminology is usually reserved for chronic diseases such as diabetes or AIDS or cardiovascular disease, not for seasonal flu or coronavirus. The prevalence is equal to the incidence times the mean survival time. Thus...

Who is the person who usually has the disease in Munchhausen Syndrome by proxy, and what...

Who is the person who usually has the disease in Munchhausen Syndrome by proxy, and what is the cause?

Sensitivity is the probability that a test will identify a person who has the disease you...

Sensitivity is the probability that a test will identify a person who has the disease you are testing for. Question 9 options: True False Which of the following statements is NOT true when describing Specificity? Question 10 options: A) It measures the effectiveness of a test in returning a negative test result to people who do not have the disease. B) It is the ability of a test to correctly identify people who have the disease you are testing for....

At one point during the COVID-19 crisis, the probability that an person who tested positive for...

At one point during the COVID-19 crisis, the probability that an person who tested positive for the illness would infect another person they came into contact with was 75% . Suppose on that day, the infected person came into contact with 15 other people. For each part below, show the formula set-up and round your final answers to four decimal places. a) The probability the ill person infected exactly 10 people out of the 15. b) the probability the ill...

The incidence of a deadly disease, among a certain population, is 0.01%. Individuals, randomly selected from...

The incidence of a deadly disease, among a certain population, is 0.01%. Individuals, randomly selected from this population are submitted to a test whose accuracy is 99% both ways. That is to say, the proportion of positive results among people known to be affected by the disease is 99%. Likewise, testing people that are not suffering from the disease yields 99% negative results. The test gives independent results when repeated. An individual test positive. a) What is the probability that...

For a certain group of individuals, the average heart rate is 80 beats per minute, with...

For a certain group of individuals, the average heart rate is 80 beats per minute, with a standard deviation of 3 beats. If a subject is selected at random, find the following, show your work: a. between 75 and 85 beats per minute. b. between 81 and 86 beats per minute. c. between 76 and 79 beats per minute.