Are there any outliers?
A. Yes, the outlier(s) is/are 36.
B. No, there are no outliers.
Describe the shape of the distribution based on the results from parts (b) and (c).
Skewed right
Bell-shaped
Skewed left
Uniform
Determine the sample standard deviation and interquartile range.
The standard deviation is $13.60$ and the interquartile range is $17.50$.
What is the probability a randomly selected student fails the homework (scores less than 70)?
Answer (2)
The probability that a randomly selected student fails the homework (scores less than 70) is approximately 0.2564, or 25.64%. This result is obtained by counting the scores below 70 and dividing by the total number of scores. Therefore, about 26% of students are likely to score below 70.
;
Count scores less than 70: There are 10 scores.
Divide by the total number of scores (39) to find the probability: 39 10 .
Calculate the decimal value: 39 10 ≈ 0.2564 .
The probability that a randomly selected student scores less than 70 is: 0.2564 .
Explanation
Analyze the problem and data We are given a dataset of homework scores and asked to find the probability that a randomly selected student scores less than 70. The dataset contains 39 scores: 36, 48, 55, 59, 63, 65, 65, 66, 66, 69, 72, 76, 77, 77, 78, 78, 78, 79, 79, 79, 79, 82, 82, 83, 85, 85, 86, 86, 87, 89, 89, 91, 91, 92, 92, 94, 96, 97, 98.
Count scores less than 70 First, we need to count how many scores are less than 70. These scores are: 36, 48, 55, 59, 63, 65, 65, 66, 66, 69. There are 10 scores less than 70.
Calculate the probability Next, we divide the number of scores less than 70 by the total number of scores to find the probability. The total number of scores is 39. So the probability is: 39 10 ≈ 0.2564
State the final answer Therefore, the probability that a randomly selected student fails the homework (scores less than 70) is approximately 0.2564.
Examples
Imagine you're a teacher trying to understand how many students might need extra help. Knowing the probability that a student scores below a certain grade helps you allocate resources effectively. For example, if you know that about 26% of students are likely to score below 70, you can plan to offer additional tutoring or review sessions. This helps ensure that more students succeed in the course.
