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 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 0.136. part 1 / 3 part 2 of 3 construct the probability distribution for the given data. x 4 5 6 7 8 p(x)

Explanation:

Step1: Recall probability distribution property

The sum of all probabilities in a probability - distribution is 1. Let \(P(4)\), \(P(5)\), \(P(6)\), \(P(7)\), \(P(8)\) be the probabilities of seeing 4, 5, 6, 7, 8 students respectively. So \(P(4)+P(5)+P(6)+P(7)+P(8) = 1\).

Step2: Substitute known values

We know that \(P(4)=0.113\), \(P(5)=0.143\), \(P(6)=0.285\), \(P(7)=0.323\). Then \(P(8)=1-(P(4)+P(5)+P(6)+P(7))\).

Step3: Calculate \(P(8)\)

\[

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

\]
For part 2:
The probability distribution is:

\(X\)	4	5	6	7	8

Answer:

For part 1: 0.136
For part 2:

\(X\)	4	5	6	7	8