Question

1. a survey of 36 local trampoline parks was conducted on their admission prices. the results are show in the box plot below. a. what percentage of trampoline parks charge over $19.75 for admission? b. what percentage of trampoline parks charge under $20.50 for admission? c. how many trampoline parks charge between $15.25 and $18.25? d. how many trampoline parks charge under $20.00? e. what is the 5 - number summary of the box plot above?

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box represents the inter - quartile range (IQR), with the left edge of the box being the first quartile ($Q_1$), the line inside the box being the median ($Q_2$), and the right edge of the box being the third quartile ($Q_3$). The whiskers extend to the minimum and maximum values.

Step2: Analyze part a

The value $19.75$ is $Q_3$. Since $Q_3$ represents the 75th percentile, the percentage of trampoline parks that charge over $19.75$ is $100 - 75=25\%$.

Step3: Analyze part b

The value $20.50$ is the maximum value. So, 100% of the trampoline parks charge under $20.50$.

Step4: Analyze part c

The proportion of data between $15.25$ (minimum) and $18.25$ ($Q_1$) is 25%. The number of parks is $n = 36$. So the number of parks charging between $15.25$ and $18.25$ is $0.25\times36 = 9$.

Step5: Analyze part d

The value $20.00$ is between $Q_3$ and the maximum. Since $Q_3$ is the 75th percentile and the maximum is the 100th percentile, and assuming a uniform distribution between $Q_3$ and the maximum, we note that all 36 parks charge under $20.00$ (because the maximum is $20.50$).

Step6: Analyze part e

The 5 - number summary consists of the minimum, $Q_1$, median ($Q_2$), $Q_3$, and maximum. From the box - plot:
Minimum: $15.25$
$Q_1$: $18.25$
Median ($Q_2$): $19.00$
$Q_3$: $19.75$
Maximum: $20.50$

Answer:

a. 25%
b. 100%
c. 9
d. 36
e. Minimum: $15.25$, $Q_1$: $18.25$, Median: $19.00$, $Q_3$: $19.75$, Maximum: $20.50$