Final answer:
The mean number of hours of sunshine per day is 3.98 hours. The standard deviation of the distribution is approximately 0.7451 hours.
Step-by-step explanation:
To calculate the mean number of hours of sunshine per day, we add up the total number of hours of sunshine over the ten days and divide by the number of days. In this case, the sum is 39.8 hours (3 + 4.5 + 5 + 5.2 + 4.8 + 4.2 + 3.8 + 3.5 + 3.2 + 4.6) and there are 10 days, so the mean is 39.8/10 = 3.98 hours per day.
To calculate the standard deviation of the distribution, we first calculate the deviation from the mean for each day by subtracting the mean from each individual data point. Then, we square each deviation, sum them up, divide by the number of days, and take the square root. In this case, the deviations from the mean are -0.98, 0.52, 1.02, 1.22, 0.82, 0.22, 0.18, 0.52, 0.78, and -0.38. When we square these deviations, we get 0.9604, 0.2704, 1.0404, 1.4884, 0.6724, 0.0484, 0.0324, 0.2704, 0.6084, and 0.1444. The sum of these squared deviations is 5.5532. Dividing by the number of days (10) gives us a variance of 0.55532. Finally, we take the square root of the variance to get the standard deviation, which is approximately 0.7451 hours.