Question

NO LINKS!! URGENT HELP PLEASE!!!

Determine if the scenario involves mutually exclusive events.

32. A cooler contains 12 bottles of sports drinks: 4 lemon-lime flavored, 3 orange-flavored, and 5 fruit-punch flavored. You grab a bottle. It is a lemon-lime or an orange.

33. Find the 5 number summary (Min, Q1, Median, Q3, Max) for the following data and draw a box and whisker graph.

18, 24, 28, 28, 36, 44, 50, 67

Answer 1

Answer:

32)  7/12 ≈ 58.3%

33)  Min = 18
       Q1 = 26
       Median = 32
       Q3 = 47
       Max = 67

Step-by-step explanation:

Question 32

To determine the probability of grabbing a lemon-lime or an orange-flavored bottle from the cooler, we need to calculate the number of favorable outcomes and the total number of possible outcomes.

In the given scenario, there are 4 lemon-lime flavored bottles and 3 orange-flavored bottles in the cooler, plus 5 fruit-punch flavored bottles. Therefore:

• Number of favorable outcomes = 4 + 3 = 7
• Total number of bottles = 4 + 3 + 5 = 12

The probability of grabbing a lemon-lime or an orange-flavored bottle is:

$\begin{aligned}\sf Probability &= \sf \dfrac{Favorable\;outcomes}{Total\; outcomes}\\\\&=\dfrac{7}{12}\\\\& \approx 58.3\%\end{aligned}$

$\hrulefill$

Question 33

The five-number summary is a statistical summary of a dataset that includes the minimum and maximum values, the median (middle value), and the first and third quartiles. It provides a concise overview of the distribution and central tendency of the data.

First, sort the given data in ascending order (this has already been done for us):

• 18, 24, 28, 28, 36, 44, 50, 67

Minimum value

The minimum value is the smallest value in the data set.

$\boxed{\sf Minimum \; value = 18}$

Median

The median is the middle value of the sorted data.

In this case, we have 8 data points, so the median is the average of the two middle values:

$\boxed{\sf Median\;(Q_2)=\dfrac{28+36}{2}=32}$

First Quartile (Q₁)

The first quartile is the median of the lower half of the data.

In this case, we have 4 data points in the lower half (18, 24, 28, 28), so the median is the average of the two middle values:

$\boxed{\sf First \;Quartile\;(Q_1)=\dfrac{24+28}{2}=26}$

Third Quartile (Q₁)

The third quartile is the median of the upper half of the data.

In this case, we have 4 data points in the upper half (36, 44, 50, 67), so the median is the average of the two middle values:

$\boxed{\sf Third\;Quartile\;(Q_3)=\dfrac{44+50}{2}=47}$

Maximum value

The maximum value is the largest value in the data set.

$\boxed{\sf Maximum\; value = 67}$

Therefore, the five-number summary for the given data set is:

• Min = 18
• Q₁ = 26
• Median = 32
• Q₃ = 47
• Max = 67

To construct the box and whisker graph (attached):

• Draw a box from the lower quartile (26) to the upper quartile (47).
• Add the median (32) as a vertical line through the box.
• The whiskers are horizontal lines from each quartile to the minimum (18) and maximum values (67).