1. **Problem Statement:** Paula recorded the number of phone calls she received each day over a period of consecutive days. We need to find: a) The total number of days the survey lasted. b) The total number of calls received over this period. c) The estimated probabilities of receiving: i) No phone calls on a particular day. ii) 5 or more phone calls on a particular day. iii) Less than 3 phone calls on a particular day. 2. **Understanding the Graph:** - The x-axis represents the number of calls per day (from 0 to 8). - The y-axis represents the number of days Paula received that many calls. - For example, the bar at 0 calls has height 2, meaning Paula received 0 calls on 2 days. 3. **Step a) Total number of days:** Add all the days for each call count: $$2 + 7 + 11 + 8 + 7 + 4 + 3 + 0 + 1 = 43$$ So, the survey lasted for **43 days**. 4. **Step b) Total number of calls:** Multiply each number of calls by the number of days and sum: $$0 \times 2 + 1 \times 7 + 2 \times 11 + 3 \times 8 + 4 \times 7 + 5 \times 4 + 6 \times 3 + 7 \times 0 + 8 \times 1$$ $$= 0 + 7 + 22 + 24 + 28 + 20 + 18 + 0 + 8 = 127$$ Paula received a total of **127 calls** over the 43 days. 5. **Step c) Estimating probabilities:** Probability is estimated as \(\frac{\text{number of days with event}}{\text{total days}}\). i) No phone calls (0 calls): $$P(0) = \frac{2}{43} \approx 0.0465$$ ii) 5 or more calls (5, 6, 7, 8 calls): Number of days = 4 + 3 + 0 + 1 = 8 $$P(\geq 5) = \frac{8}{43} \approx 0.1860$$ iii) Less than 3 calls (0, 1, 2 calls): Number of days = 2 + 7 + 11 = 20 $$P(<3) = \frac{20}{43} \approx 0.4651$$ **Summary:** - Survey lasted 43 days. - Total calls received: 127. - Probability of no calls on a day: about 4.65%. - Probability of 5 or more calls: about 18.60%. - Probability of less than 3 calls: about 46.51%.