Final answer:
The probability can be calculated using the binomial probability formula. It requires summing probabilities from 71 to 173. Online calculators or statistical software can simplify the calculation.
Step-by-step explanation:
The probability that more than 70 but fewer than 174 households in a random sample of 174 households will have personal computers can be calculated using the binomial probability formula:
P(X=k) = C(n,k) imes p^k imes (1-p)^(n-k)
In this case, n=174 and p is the proportion of households that have personal computers. To find the probability, you need to calculate the sum of probabilities for k=71 to 173, which can be quite time-consuming. However, you can use an online binomial probability calculator or statistical software like Excel to find the probability directly.