A certain hotel has 80 rooms. Based on many previous years' occupancy rates, the owners of the hotel constructed the table below showing the daily occupancy rates and their probabilities of occuring for the coming summer season. Based on the probability distribution in the table, to the nearest whole number, what is the expected number of rooms that will be occupied on any day during the coming summer season?

$$ \begin{array} {|c|c|} \hline \text{Occupancy rate} & \text{Probability} \\ \hline 0.60 & 0.20 \\ 0.70 & 0.40 \\ 0.80 & 0.30 \\ 0.90 & 0.10 \\ \hline \end{array} $$

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We can calculate the expected occupancy rate by taking the sum of the products of occupancy rate and probability:

$$ 0.60(0.20) + 0.70(0.40) + 0.80(0.30) + 0.90(0.10) $$ $$ = 0.12 + 0.28 + 0.24 + 0.09 $$ $$ = 0.73 $$

We can then estimate that with an occupancy rate of \(0.73\),

$$ 80(0.73) =58.4 \approx \boxed{58} $$