(a)
To calculate: The probability that the student eats regularly in the cafeteria and is not a
(a)
Answer to Problem T5.11SPT
The probability that the student eats regularly in the cafeteria and is not a
Explanation of Solution
Given information: Below is the table of the division of students
Grade | ||||||
9th | 10th | 11th | 12th | Total | ||
Eat in cafeteria | Yes | 130 | 175 | 122 | 68 | 495 |
No | 18 | 34 | 88 | 170 | 310 | |
Total | 148 | 209 | 210 | 238 | 805 |
Total number of students
Formula used:
P (a student eats regularly in the cafeteria
Calculation:
From the given information,
Number of students who eats regularly in the cafeteria and is a 9th grader
Number of students who eats regularly in the cafeteria and is a 11th grader
Number of students who eats regularly in the cafeteria and is a 12th grader
So, P (a student eats regularly in the cafeteria
(b)
To calculate: The probability that a student is a 10th grader given the students eats regularly in the cafeteria.
(b)
Answer to Problem T5.11SPT
The probability that a student is a 10th grader given the students eats regularly in the cafeteria is 0.3535.
Explanation of Solution
Formula used:
P (a student is a 10th grader
P (eats regularly at a cafeteria)
P (a student is a 10th grader
Calculation:
P (a student is a 10th grader
P (eats regularly at a cafeteria)
P (a student is a 10th grader | eats regularly at a cafeteria)
(c)
To check: Whether the events “10th grader” and “eats regularly in the cafeteria” are independent.
(c)
Answer to Problem T5.11SPT
The events “10th grader” and “eats regularly in the cafeteria” are not independent.
Explanation of Solution
Formula used:
Condition for independence
Calculation:
Number of students in 10th grade
Number of students who eat regularly in the cafeteria
Number of students who are in 10th grade and eat regularly in the cafeteria
So, P (10th grade)
P (eats regularly in the cafeteria)
P (10th grader and eats regularly in the cafeteria)
Checking condition of independence
Chapter 5 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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