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tresset_1 [31]
3 years ago
14

If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 477 viruses would d

iffer from the population proportion by more than 3%.
Mathematics
1 answer:
melisa1 [442]3 years ago
3 0

Answer:

0.01596

Step-by-step explanation:

A scientist claims that 8% of the viruses are airborne

Given that:

The population proportion p = 8%

The sample size = 477

We can calculate the standard deviation of the population proportion by using the formula:

\sigma_p = \sqrt{\dfrac{p(1-p)}{n}}

\sigma_p = \sqrt{\dfrac{0.8(1-0.8)}{477}}

\sigma_p = \sqrt{\dfrac{0.0736}{477}}

\sigma_p = 0.02098

The required probability can be calculated as:

P(| \hat p - p| >  0.03) = P(\hat p - p< -0.03 \ or \  \hat p - p > 0.03)

= P \bigg ( \dfrac{\hat p -p }{\sqrt{\dfrac{p(1-p)}{n}}} < -\dfrac{0.03}{0.0124}  \bigg ) +  P \bigg ( \dfrac{\hat p -p }{\sqrt{\dfrac{p(1-p)}{n}}} >\dfrac{0.03}{0.0124} \bigg )

= P(Z < -2.41) + P(Z > 2.41)

= P(Z < -2.41) + P(Z < -2.41)

= 2P( Z< - 2.41)

From the  Z-tables;

P(| \hat p - p| >  0.03) = 2 ( 0.00798

P(| \hat p - p| >  0.03) = 0.01596

Thus, the required probability = 0.01596

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