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Positive test Negative test es HIV Cell A Cell B not carry HIV Cell D Cell E Cell G Cell H

Positive test Negative test es HIV Cell A Cell B not carry HIV Cell D Cell E Cell G Cell H

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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4:35 ll ( Notes February 19, 2021 at 4:35 PM Imagine a hypothetical population of 1,000,000 people for whom these percentages hold exactly. Positive test Negative test Total Carries HIV Cell A Cell B Cell C Does not carry HIV Cell D Cell E Cell F Total Cell G Cell H 1,000,000 Positive test Negative test Total Carries HIV Does not carry HIV Total 1,000,000 a) Assuming that 0.5% of the population of 1,000,000 people carries HIV, how many such carriers are there in the population? How many non-carriers are there? Record these values in the table in Cells C and F, respectively. b) Consider for now just the carriers. If 97.7% of them test positive, how many test positive? How many carriers does that leave who test negative? Record these values in the table in Cells A and B, respectively. c) Now consider only the non-carriers. If 92.6% of them test negative, how many test negative? How many non-carriers does that leave who test positive? Record these values in the table in Cells E and D, respectively. d) Determine the total number of positive test results and the total number of negative test results. Record these values in the appropriate places within the table.
Transcribed Image Text:4:35 ll ( Notes February 19, 2021 at 4:35 PM Imagine a hypothetical population of 1,000,000 people for whom these percentages hold exactly. Positive test Negative test Total Carries HIV Cell A Cell B Cell C Does not carry HIV Cell D Cell E Cell F Total Cell G Cell H 1,000,000 Positive test Negative test Total Carries HIV Does not carry HIV Total 1,000,000 a) Assuming that 0.5% of the population of 1,000,000 people carries HIV, how many such carriers are there in the population? How many non-carriers are there? Record these values in the table in Cells C and F, respectively. b) Consider for now just the carriers. If 97.7% of them test positive, how many test positive? How many carriers does that leave who test negative? Record these values in the table in Cells A and B, respectively. c) Now consider only the non-carriers. If 92.6% of them test negative, how many test negative? How many non-carriers does that leave who test positive? Record these values in the table in Cells E and D, respectively. d) Determine the total number of positive test results and the total number of negative test results. Record these values in the appropriate places within the table.
Expert Solution
Step 1

(a)

Given that the population is,

N= 1,000,000

The percentage of people carries HIV is,      0.5%

The total number of people Carries HIV from the population of 1,000,000 is,

=1000000*0.5%

=1000000*0.005

= 5000

The percentage of people does not carries HIV is ,

= 100-0.5%=99.5%

The total number of people does not Carries HIV from the population of 1,000,000 is,

=1000000*99.5%

=1000000*0.995

= 995000

The cells C and f are filled in the table below.

  Positive test Negative test Totals
Carries HIV cell A cell B  5000
Does not Carries HIV cell D cellE  995000
Totals cell G cell H 1000000
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