In: Statistics and Probability
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.
P(airborne virus), p = 0.08
q = 1 - p = 0.92
Sample size, n = 719
P( < A) = P(Z < (A - )/)
= p = 0.08
=
=
= 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