uppose that we have test for lung cancer, which correctly identifies those with the cancer 70 % of the time, and mistakenly identifies those without the cancer 5 % of the time. In the cohort of interest, the rate of this cancer is somewhat low: 0.9 %. Find the probability -- a number between 0 and 1 -- that someone diagnosed (testing positive) with this test actually has lung cancer.

uppose that we have test for lung cancer, which correctly identifies those with the cancer 70 % of the time, and mistakenly identifies those without the cancer 5 % of the time. In the cohort of interest, the rate of this cancer is somewhat low: 0.9 %. Find the probability -- a number between 0 and 1 -- that someone diagnosed (testing positive) with this test actually has lung cancer.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A company estimates that 0.7% of their products will fail after the original warrantyperiod but within 2 years of the purchase, with a replacement cost of $350. If they offer a2-year extended warranty for $48, what is the company's expected value of each warrantysold?
Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 221 numerical entries from the file and r = 51 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.(i) Test the claim that p is less than 0.301. Use ? = 0.10.
An electronics company had sales of $25,000,000 in the year just completed. Sales are expected to decline by 3% per year for the next three years un�l new drugs, now under development, receive regulatory approval. Then sales should grow at 7% per year for the next four years. What are the expected sales for the final year of the seven-year period? [
Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 221 numerical entries from the file and r = 51 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.(i) Test the claim that p is less than 0.301. Use ? = 0.05. What is the value of the sample test statistic? (Round your answer to two decimal places.)=___(c) Find the P-value of the test statistic. (Round your answer to four decimal places.) =____
Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.306. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 219 numerical entries from the file and r = 49 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.Test the claim that p is less than 0.306. Use ? = 0.05. (a) What is the level of significance?State the null hypothesis H0 and the alternate hypothesis H1 . H0 : p H1 : p (b) What sampling distribution will you use? The Student's tThe standard normal since np…
A company estimates that 0.7% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $400. If they offer a 2 year extended warranty for $27, what is the company's expected value of each warranty sold?
The magnitudes of earthquakes recorded in a region of North America can be modeled by an exponential distribution with a mean of 2.4 as measured on the Righter scale. Of the next 10 earthquakes to strike this region, find the probability that at least one will exceed 5.0 on the Richter scale.
The waiting time at a railroad crossing follows an exponential distribution, with an average time of 8 minutes, determining the probability of waiting between 2 and 5 minutes.
In the game of roulette, a player can place a $5 bet on the number 34 and have a 1/38 probability of winning. If the metal ball lands on 34, the player gets to keep the $5 paid to play the game and the player is awared an additional $175. Otherwise, the player is awarded nothing and the casino takes the player's $5. Find the average expected E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. What is the expected value?
Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 215 numerical entries from the file and r = 50 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.(i) Test the claim that p is less than 0.301. Use ? = 0.10. (a) What is the level of significance?State the null and alternate hypotheses. H0: p = 0.301; H1: p < 0.301H0: p < 0.301; H1: p = 0.301 H0: p = 0.301; H1: p > 0.301H0: p = 0.301; H1: p ≠ 0.301 (b) What sampling…
Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 215 numerical entries from the file and r = 50 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. (b) What sampling distribution will you use? The Student's t, since np > 5 and nq > 5.The standard normal, since np < 5 and nq < 5. The standard normal, since np > 5 and nq > 5.The Student's t, since np < 5 and nq < 5. What is the value of the sample test…
You are pricing a permanent disability insurance using the following model with transition forces: Healthy 0.01 Disabled 1 0.06 0.04 Dead Calculate the probability that a healthy life on November 1, 2013 will become disabled between November 1, 2017 and November 1, 2020. A 0.018 0.020 Previous Overview Next