Your neighborhood gym tracked how many days each of its members worked out over the past week. Let G = the
number of days per week a member worked out.
Number of Days
0
1
2 3
4
5
6
7
Probability 0.49 0.12 0.13 0.15 0.06 0.02 0.02 0.01
Calculate and interpret the mean of G
Each member of the gym worked out about 3.5 days per week.
Each member of the gym worked out 1.36 days per week
If many, many members were randomly selected, the average number of days per week a member worked out
would be about 1.36 days.
If many, many members were randomly selected, the average number of days per week a member worked out
would be about 3 days.

Question

Today at 4:54 AM
Mathematics

Answered

Your neighborhood gym tracked how many days each of its members worked out over the past week. Let G = the
number of days per week a member worked out.
Number of Days
0
1
2 3
4
5
6
7
Probability 0.49 0.12 0.13 0.15 0.06 0.02 0.02 0.01
Calculate and interpret the mean of G
Each member of the gym worked out about 3.5 days per week.
Each member of the gym worked out 1.36 days per week
If many, many members were randomly selected, the average number of days per week a member worked out
would be about 1.36 days.
If many, many members were randomly selected, the average number of days per week a member worked out
would be about 3 days.

Answer :

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alexfarmand001 alexfarmand001 · Answer 1 · 2025-03-31T04:59:49-04:00

alexfarmand001 alexfarmand001

Today at 4:59 AM

Answer:

C.

If many, many members were randomly selected, the average number of days per week a member worked out would be about 1.36 days.

Step-by-step explanation:

yes

Answer Link

astha8579 astha8579 · Answer 2 · 2025-03-31T04:59:37-04:00

You can use the definition of weighted mean (expectation) to calculate the mean of "G".

The mean of "G" is 1.36 days

It is interpreted as

Option C: If many, many members were randomly selected, the average number of days per week a member worked out

would be about 1.36 days.

How to calculate the expectation of a discrete random variable?

Expectation can be taken as a weighted mean, weights being the probability of occurrence of that specific observation.

Thus, if the random variable is X, and its probability is[tex]f(x) = P(X = x)[/tex], then,

[tex]E(X) = \sum_{i=1}^n( f(x_i) \times x_i)[/tex] (n is number of values X takes)

Using above method to calculate the mean of "G"

"G" = number of days per week a member worked out

Mean of "G" = E("G") = [tex]= 0 \times 0.49 + 1 \times 0.12 + 2 \times 0.13 + 3 \times 0.15 + 4 \times 0.06 + 5 \times 0.02 + 6 \times 0.02 + 7 \times 0.01\\= 1.36[/tex]

This is the mean value of "G". Since "G" was tracking the number of days per week a member worked out, thus, mean of "G" = 1.36 is showing that, on average, a member worked out 1.36 days per week.

Option third is correct in this case, since for large random sample, the mean of the sample will coincide with the population mean(by Central limit theorem)

If many, many members were randomly selected, the average number of days per week a member worked out

would be about 1.36 days.

Thus,

The mean of "G" is 1.36 days

It is interpreted as

Option C: If many, many members were randomly selected, the average number of days per week a member worked out

would be about 1.36 days.

Learn more about expectation here:

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