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In a particular illness , a false-positive result is obtained about 1 in 125 times the test is administered. If the test is administered to 15,000 people, estimate the probabilty of there being more than 135 false-positive results.
(HINT: use the normal approximation to the binomial distribution)

Respuesta :

Answer:

0.0778

Step-by-step explanation:

Probability of false positive result, p = [tex]\frac{1}{125}[/tex] = 0.008

Sample size, n = 15,000

mean, μ = np = 15000 × 0.008 = 120

Now,

Standard deviation, σ = [tex]\sqrt{np(1-p)}[/tex]

or

=  [tex]\sqrt{15,000\times0.008(1-0.008)}[/tex]

= 10.91

Now,

Probability of there being more than 135 false-positive results

= P(X > 135) ≈ [tex]P(\frac{X-\mu}{\sigma}>\frac{135-120}{10.91})[/tex]

or

= P(z > 1.42)

or

= 1 - P(z ≤ 1.42)

= 1 - 0.9222                 [P(z ≤ 1.42) = 0.9222 from standard z table]

= 0.0778

Hence,

P(X > 135) = 0.0778

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