2. The probabilities that a surgeon operates on 3, 4, 5, 6 or 7 patients in any day are 0.15, 0.10, 0.20, 0.25 and 0.30 respectively. Find the average number of patients that a surgeon operates on a day.
3. A researcher conducted a study to investigate how a newborn baby’s crying after midnight affects the sleep of the baby's mother. The researcher randomly selected 50 new mothers and asked how many times they were awakened by their newborn baby's crying after midnight per week. Two mothers were awake zero times, 11 mothers were awake one time, 23 mothers were awake two times, nine mothers were awake three times, four mothers were awakened four times, and one mother was awake five times. Find the expected value of the number of times a newborn baby's crying wakes its mother after midnight per week.
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pa brainliest poTo find the average number of patients that a surgeon operates on a day, we need to multiply each number of patients by its probability, and then add up the results:
(3 × 0.15) + (4 × 0.10) + (5 × 0.20) + (6 × 0.25) + (7 × 0.30) = 0.45 + 0.40 + 1.00 + 1.50 + 2.10 = 4.45
Therefore, the average number of patients that a surgeon operates on a day is 4.45.
To find the expected value of the number of times a newborn baby's crying wakes its mother after midnight per week, we need to multiply each number of times by its probability, and then add up the results:
(0 × 2/50) + (1 × 11/50) + (2 × 23/50) + (3 × 9/50) + (4 × 4/50) + (5 × 1/50) = 0 + 0.22 + 0.92 + 0.54 + 0.16 + 0.02 = 1.86/week
Therefore, the expected value of the number of times a newborn baby's crying wakes its mother after midnight per week is 1.86