A scientist claims that 8% of viruses are airborne. If the scientist is accurate, what is...

A scientist claims that 8% of viruses are airborne.

If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 719 viruses would differ from the population proportion by greater than 3%? Round your answer to four decimal places.

Solutions

Expert Solution

P(airborne virus), p = 0.08

q = 1 - p = 0.92

Sample size, n = 719

P( < A) = P(Z < (A - $\mu_\hat{p}$ )/ $\sigma_\hat{p}$ )

$\mu_\hat{p}$ = p = 0.08

$\sigma_\hat{p}$ =

= 0.0101

P(proportion of airborne viruses in a sample of 719 viruses would differ from the population proportion by greater than 3%) = P( < (0.08-0.03)) + P( > (0.08+0.03))

= P( < 0.05) + P( > 0.11)

= P( < 0.05) + 1 - P( < 0.11)

= P(Z < (0.05-0.08)/0.0101) + 1 - P(Z < (0.11-0.08)/0.0101)

= P(Z < -2.97) + 1 - P(Z < 2.97)

= 0.0015 + 1 - 0.9985

= 0.0030

orchestra answered 1 year ago

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