Question

algebra 2b
lep 5
statistics
lep goals
in this lep, students will:
understand statistics as a process for making inferences about population parameters based on a
random sample from that population.
use the mean and standard deviation of a data set to fit a normal distribution and to estimate population
percentages.
decide if a specified model is consistent with results from a given data - generating process.
use data from a sample survey to estimate a population mean or proportion; develop a margin of error
with the use of simulation models for random sampling.
engage
module 22 - gathering and displaying data
essential question: how can gathering and displaying data help to solve real - world problems?
are you ready? #22 - complete these exercises to review skills you will need for this module.
two - way tables
example 1
the table shows the number of tickets sold
for seats in the four areas of the local
playhouse for showings in a three - day
period. what percent of the tickets
sold for the saturday showing were for
orchestra level seating?
saturday is the second to last column.
the total tickets sold for the
saturday performance were
4 + 891+540 + 695, which is a total
of 2130 tickets. the percent of those
tickets that were orchestra level is
\\( \frac { 891 } { 2130 } \cdot 100 \\), or about 42%.
use the table shown to find each percent.

1. what percent of all the loge 2. what percent of all tickets sold 3. what percent of all tickets sold

tickets sold were for the friday were for the sunday showing? were for seats at either the loge
showing? or balcony level?

Explanation:

Step1: Calculate total loge tickets

Total loge tickets = \(492 + 540+411=1443\)

Step2: Calculate loge tickets for Friday

Loge tickets for Friday = \(492\)

Step3: Calculate the percentage

Percentage \(=\frac{492}{1443}\times100\approx34.1\%\)

Step4: Calculate total tickets

Total tickets \(=12 + 4+2+856 + 891+773+492 + 540+411+712 + 695+359\)
\(=12+4+2+(856 + 891+773)+(492 + 540+411)+(712 + 695+359)\)
\(=18+(2520)+(1443)+(1766)\)
\(=18 + 2520+1443+1766=5747\)

Step5: Calculate Sunday tickets

Sunday tickets \(=2 + 773+411+359=1545\)

Step6: Calculate Sunday tickets percentage

Percentage \(=\frac{1545}{5747}\times100\approx26.9\%\)

Step7: Calculate loge and balcony tickets

Loge and balcony tickets \(=(492 + 540+411)+(712 + 695+359)\)
\(=1443+1766 = 3209\)

Step8: Calculate loge and balcony percentage

Percentage \(=\frac{3209}{5747}\times100\approx55.8\%\)

Answer:

1. Approximately \(34.1\%\)
2. Approximately \(26.9\%\)
3. Approximately \(55.8\%\)