Studying Refer to the data set in Exercise 23 and the box-and-whisker plot you drew that represents the data set.


c. You randomly select one student from the sample. What is the likelihood that the student studied less than 2 hours per day? Write your answer as a percent.

Verified step by step guidance

1. Step 1: Review the box-and-whisker plot you created for the data set in Exercise 23. Identify the range of values represented on the plot, including the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
2. Step 2: Determine the portion of the data that represents students who studied less than 2 hours per day. This can be done by identifying where the value of 2 hours falls on the box-and-whisker plot relative to the quartiles.
3. Step 3: Calculate the percentage of the data that falls below 2 hours. If 2 hours is less than Q1, for example, then the percentage of students studying less than 2 hours would correspond to the proportion of the data below Q1 (typically 25%).
4. Step 4: If the value of 2 hours falls within a specific quartile range, use the distribution of data within that range to estimate the percentage of students studying less than 2 hours. For example, if 2 hours is between Q1 and the median, you would estimate the proportion of data in that segment.
5. Step 5: Convert the proportion of students studying less than 2 hours into a percentage by multiplying the proportion by 100. Write your final answer as a percentage.

Key Concepts

Box-and-Whisker Plot

A box-and-whisker plot is a graphical representation of a data set that displays its minimum, first quartile, median, third quartile, and maximum. It helps visualize the distribution and identify outliers. Understanding this plot is crucial for interpreting the data set and determining the range of study hours.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1 or as a percentage. In this context, it involves calculating the proportion of students who studied less than 2 hours per day relative to the total number of students in the sample.

Percentages

A percentage is a way of expressing a number as a fraction of 100, which is useful for comparing proportions. In this question, converting the probability of selecting a student who studied less than 2 hours into a percentage allows for a clearer understanding of the likelihood in a familiar format.