Find the best solutions to your problems with the help of IDNLearn.com's expert users. Ask any question and receive timely, accurate responses from our dedicated community of experts.
Find the probability that a student selected at random from the class scored:
Given the marks scored by 40 students in an objective test out of 40:
Total number of students: [tex]\[ 2 + 5 + 9 + 6 + 3 + 4 + 5 + 1 = 35 \][/tex]
Let's calculate the probabilities for each part:
a) Marks greater than 28:
Students who scored greater than 28 are those who scored 33 or 38. The number of such students is [tex]\(5 + 1 = 6\)[/tex].
Probability (P) is given by: [tex]\[ \text{P(marks > 28)} = \frac{\text{Number of students who scored more than 28}}{\text{Total number of students}} = \frac{6}{35} \approx 0.1714 \][/tex]
b) Marks less than 28:
Students who scored less than 28 are those who scored 3, 8, 13, 18, or 23. The number of such students is [tex]\(2 + 5 + 9 + 6 + 3 = 25\)[/tex].
Probability (P) is given by: [tex]\[ \text{P(marks < 28)} = \frac{\text{Number of students who scored less than 28}}{\text{Total number of students}} = \frac{25}{35} \approx 0.7143 \][/tex]
c) Scored 33 marks:
The number of students who scored exactly 33 marks is [tex]\(5\)[/tex].
Probability (P) is given by: [tex]\[ \text{P(marks = 33)} = \frac{\text{Number of students who scored 33}}{\text{Total number of students}} = \frac{5}{35} \approx 0.1429 \][/tex]
d) Between 3 and 33 marks (inclusive):
Students who scored between 3 and 33 marks include those who scored 3, 8, 13, 18, 23, 28, and 33. The number of such students is [tex]\(2 + 5 + 9 + 6 + 3 + 4 + 5 = 34\)[/tex].
Probability (P) is given by: [tex]\[ \text{P(3 ≤ marks ≤ 33)} = \frac{\text{Number of students who scored between 3 and 33 (inclusive)}}{\text{Total number of students}} = \frac{34}{35} \approx 0.9714 \][/tex]
In summary, the probabilities are: a) [tex]\( \approx 0.1714 \)[/tex] b) [tex]\( \approx 0.7143 \)[/tex] c) [tex]\( \approx 0.1429 \)[/tex] d) [tex]\( \approx 0.9714 \)[/tex]
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.
