Question

the data shows the number of hours spent studying per day by a sample of 28 students. use the box - and - whisker plot below to answer parts (1) through (3) here.

(1) about 75% of the students studied no more than how many hours per day?
(2) what percent of the students studied more than 3.5 hours per day?
(3) you randomly select one student from the sample. what is the likelihood that the student studied less than 0.5 hour per day?

Explanation:

Step1: Recall quartile concept

For a box - and - whisker plot, the third quartile ($Q_3$) represents the value below which 75% of the data lies.

Step2: Analyze data for 75% value

We need to find the value of $Q_3$ from the data set used to create the box - and - whisker plot.

Step3: Recall percentage above a value

To find the percentage of students who studied more than 3.5 hours per day, we first need to order the data and count the number of data points above 3.5 and divide by the total number of data points (28 in this case) and multiply by 100.

Step4: Recall probability formula

The probability that a student studied less than 0.5 hour per day is the number of data points less than 0.5 divided by the total number of data points (28), which is $\frac{\text{Number of data points}<0.5}{28}$

However, since the data values from the sample are not clearly visible in the provided image, let's assume we have the ordered data set $x_1,x_2,\cdots,x_{28}$.

1. For the value below which 75% of students studied:

• First, we find the position of the third - quartile. The position of $Q_3$ for a data set of size $n = 28$ is $i=\frac{3(n + 1)}{4}=\frac{3\times(28+1)}{4}=\frac{3\times29}{4}=21.75$.
• We then interpolate between the 21st and 22nd ordered data values. If the 21st value is $a$ and the 22nd value is $b$, then $Q_3=a+(0.75)(b - a)$.

1. For the percentage of students who studied more than 3.5 hours per day:

• Count the number of data points $n_{>3.5}$ in the data set that are greater than 3.5. Then the percentage $P=\frac{n_{>3.5}}{28}\times100$.

1. For the probability that a student studied less than 0.5 hour per day:

• Count the number of data points $n_{<0.5}$ in the data set that are less than 0.5. Then the probability $P=\frac{n_{<0.5}}{28}$.

Since we don't have the actual data values:

Answer:

1. Without the data, we cannot give a numerical answer for the value below which 75% of students studied.
2. Without counting the number of data points above 3.5, we cannot give a numerical answer for the percentage of students who studied more than 3.5 hours per day.
3. Without counting the number of data points below 0.5, we cannot give a numerical answer for the probability that a student studied less than 0.5 hour per day.