Question

A scientist claims that 6% of viruses are airborne. If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 403 viruses would differ from the population proportion by greater than 3%? Round your answer to four decimal places.

Answer 1

P(a virus is airborne), p = 0.06

q = 1 - p = 0.94

n = 403

P( < A) = P(Z < (A - )/)

= p = 0.06

=

=

= 0.01183

P(sample would differ from the population proportion by greater than 3%) = P(Z < -0.03/) + P(Z > 0.03/)

= P(Z < -0.03/0.01183) + P(Z > 0.03/0.01183)

= P(Z < -2.54) + P(Z > 2.54)

= P(Z < -2.54) + 1 - P(Z < 2.54)

= 0.0055 + 1 - 0.9945

= 0.0110