*label*Mathematics

### Question Description

1. You randomly survey people in the mall about whether or not they regularly use text messaging. The results are shown in the tally sheets below based on the people’s ages.

- Make a two-way table that includes the marginal frequencies.
- Make a two-way table that shows both the joint and marginal relative frequencies. Round to the nearest hundredth, if necessary.
- What is the probability that someone who is between the ages of 20-29 also texts regularly?
- What is the probability that someone who is between the ages of 40-49 also texts regularly?
- Does the data show a relationship between age and texting? Explain.

2. The data below represents the number of hits on your web site over 10 months.

- Make a scatter plot of ln y versus x. Use the scatter plot to find the equation for the line of best fit.
- Make a scatter plot of ln y versus ln x. Use the scatter plot to find the equation for the line of best fit.
- Based on your answers in part a and b, would an exponential model or a power model be better to represent this data? Explain.
- Use your answers from parts a and b to find an exponential model and a power model to represent this data by hand.
- Use the regression feature on your calculator to find an exponential model and a power model to represent this data.
- Use your answer from parts c and d to make the best estimate for the number of hits your web site will have in 12 months.

## Tutor Answer

HiKindly see attached file with step by step solution of both problems together with a plagiarism report in case you need to present it

1. The table of marginal frequencies is obtained by counting the different tallies obtained

for each group and calculating the respective subtotal and total frequencies. Taking

this into account,

20-29

30-39

40-49

TOTAL

The person texts

regularly

25

11

2

38

The person does not

text regularly

7

13

10

30

TOTAL

32

24

12

68

2. As can be observed in the table of marginal frequencies, the total number of people

participating in the survey was of 68. Taking this information into account, the table of

marginal relative frequency is obtained by dividing the frequency of each group by the

total number of people. On the other hand, the joint marginal relative frequency is

obtained by adding the marginal relative frequency of each of the data located on

either the rows or the columns. The resulting table is:

20-29

30-39

40-49

TOTAL

The person texts

regularly

0.37

0.16

0.03

0.56

The person does not

text regularly

0.10

0.19

0.15

0.44

TOTAL

0.47

0.35

0.18

1.00

3. The conditional probability that somebody texts regularly assuming he is between 20

and 29 years of age is given by:

𝑝(𝐴 ∩ 𝐵)

𝑝(𝐴|𝐵) =

𝑝(𝐵)

Considering that the probability that somebody is between 20 and 29 years of age

(p(B)) is 0.47 and the probability that somebody is between 20 and 29 years of ...

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