Step 1 :Given that 290 people have been exposed to the flu, and the probability that a person contracts the flu on exposure is 0.43.
Step 2 :We are asked to find the variance of these 290 people contracting the flu.
Step 3 :The variance of a binomial distribution is given by the formula \(npq\), where \(n\) is the number of trials, \(p\) is the probability of success, and \(q\) is the probability of failure (\(1-p\)).
Step 4 :In this case, \(n=290\), \(p=0.43\), and \(q=1-0.43=0.57\).
Step 5 :So we need to calculate \(290*0.43*0.57\).
Step 6 :By calculating, we get the variance as \(71.0790\).
Step 7 :So, the variance of these 290 people contracting the flu is \(\boxed{71.0790}\).