Partiol3 Part 1 of 3 Find the probability that a tutor sees 8 students in an hour. Round your answer to three decimal places. The probability that a tutor sees 8 students in an hour is \( \square \) .

To find the probability that a tutor sees 8 students in an hour, we can use the Poisson distribution. The formula for the Poisson probability is: \[ P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!} \] where \( k \) is the number of events (students seen), \( \lambda \) is the average rate of events per interval (students seen per hour), and \( e \) is Euler's number (approximately 2.71828). Assuming the average rate of students seen by the tutor per hour is known (let’s say it’s 6 students/hour for this example), we plug in the values: - \( k = 8 \) - \( \lambda = 6 \) Using the formula, we calculate: \[ P(X = 8) = \frac{6^8 e^{-6}}{8!} \] Calculating \( 6^8 \), \( e^{-6} \), and \( 8! \): - \( 6^8 = 1679616 \) - \( e^{-6} \approx 0.002478752 \) - \( 8! = 40320 \) Now, substituting these values into the probability formula: \[ P(X = 8) = \frac{1679616 \times 0.002478752}{40320} \] Calculating this gives: \[ P(X = 8) \approx 0.098 \] Therefore, the probability that a tutor sees 8 students in an hour is approximately **0.098** when rounded to three decimal places.