To determine the correct distribution to find the probability that exactly 3 homes with 3 or more bedrooms will be sold tomorrow, we start by noting that the average number of such homes sold per week is given as 14.
Assuming that the sales of homes can be modeled as events occurring independently and at a consistent average rate, we should use the Poisson distribution, which is appropriate for counting the number of events in a fixed interval when the events occur with a known constant mean rate.
Since we are looking at the sales for a single day (tomorrow), we need to adjust the average from a weekly figure (14 homes per week) to a daily figure.
There are generally 7 days in a week, so the average number of homes sold per day is:
\[ \text{Mean per day} = \frac{14 \text{ homes per week}}{7 \text{ days per week}} = 2 \text{ homes per day} \]
Hence, we would use a Poisson distribution with a mean (λ) of 2 homes for tomorrow.
Thus, the correct choice is:
Poisson distribution with mean 2.
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