At the beginning of October of 2020, based upon the results of over 1.5 million antibody tests, it was determined that 27% of New York City residents had COVID-19 antibodies. Suppose we took a random sample of n=19 New York City residents at the beginning of October. Let X = the number of these selected residents who have COVID-19 antibodies. (Do not use a normal approximation for this problem. This is a binomial problem.) a) What is the probability that X < 6? b) What is the probability that 5 ≤ X ≤ 7? c) What is the probability that X = 6?

At the beginning of October of 2020, based upon the results of over 1.5 million antibody tests, it was determined that 27% of New York City residents had COVID-19 antibodies. Suppose we took a random sample of n=19 New York City residents at the beginning of October. Let X = the number of these selected residents who have COVID-19 antibodies. (Do not use a normal approximation for this problem. This is a binomial problem.) a) What is the probability that X < 6? b) What is the probability that 5 ≤ X ≤ 7? c) What is the probability that X = 6?

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...

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A paper describes a study of the use of MRI (Magnetic Resonance Imaging) exams in the diagnosis of breast cancer. The purpose of the study was to determine if MRI exams do a better job than mammograms of determining if women who have recently been diagnosed with cancer in one breast have cancer in the other breast. The study participants were 950 women who had been diagnosed with cancer in one breast and for whom a mammogram did not detect cancer in the other breast. These women had an MRI exam of the other breast, and 101 of those exams indicated possible cancer. After undergoing biopsies, it was determined that 30 of the 101 did in fact have cancer in the other breast, whereas 71 did not. The women were all followed for one year, and four of the women for whom the MRI exam did not indicate cancer in the other breast were subsequently diagnosed with cancer that the MRI did not detect. The accompanying table summarizes this information. Cancer Cancer Not Present Present Total MRI…
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