Question

mathematics tutoring center at a drop - in mathematics tutoring center, each teacher sees 4 to 8 students per hour. the probability that a tutor sees 4 students in an hour is 0.113; 5 students, 0.143; 6 students, 0.285; and 7 students, 0.323. part 1 of 1 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

Explanation:

Step1: Recall probability property

The sum of probabilities of all possible outcomes is 1. Let \(P(4)\) be the probability of seeing 4 students, \(P(5)\) be the probability of seeing 5 students, \(P(6)\) be the probability of seeing 6 students, \(P(7)\) be the probability of seeing 7 students and \(P(8)\) be the probability of seeing 8 students. Then \(P(4)+P(5)+P(6)+P(7)+P(8) = 1\).

Step2: Rearrange to find \(P(8)\)

\(P(8)=1-(P(4) + P(5)+P(6)+P(7))\). Given \(P(4) = 0.113\), \(P(5)=0.143\), \(P(6)=0.285\), \(P(7)=0.323\).

Step3: Calculate \(P(8)\)

\[

$$\begin{align*} P(8)&=1-(0.113 + 0.143+0.285+0.323)\\ &=1 - 0.864\\ &= 0.136 \end{align*}$$

\]

Answer:

0.136