In order to plan an effective intervention effort for HIV transmission in Washoe County, scientists are interested in identifying the current prevalence of injection drug users (IDU) in Washoe County. The Behavioral Risk Factor Surveillance System (BRFSS) found that national prevalence of IDU is 3%.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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In order to plan an effective intervention effort for HIV transmission in Washoe County, scientists are interested in identifying the current prevalence of injection drug users (IDU) in Washoe County. The Behavioral Risk Factor Surveillance System (BRFSS) found that national prevalence of IDU is 3%.

With a sample size of 300, what is the standard notation of the normal approximation of the binomial count?

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Step 1

Binomial Distribution: If we have n trials each having two outcomes, say Success and Failure, trials being independent and the probability of success, say p, remaining constant, then the distribution of the number of success follows binomial.

Let us assume X be a random variable denoting the number of success.

Then X~bin(n, p), n and p being the parameters of the binomial distribution.

The probability mass function of X is given by,

Statistics homework question answer, step 1, image 1

Normal Distribution: A continuous random variable X is said to follow Normal distribution with parameters μ and σ2 if its probability density function is given by,

Statistics homework question answer, step 1, image 2

It is denoted by,

Statistics homework question answer, step 1, image 3

Then by property of normal distribution,

Statistics homework question answer, step 1, image 4

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