We appreciate your visit to Your neighborhood gym tracked how many days each of its members worked out over the past week Let tex G tex represent the number of. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To calculate and interpret the mean of the number of days per week ([tex]$G$[/tex]) a gym member worked out, we use the concept of expected value in probability. Here’s how to solve it step-by-step:
1. Identify the Number of Days and their Probabilities:
We have the number of days members worked out and their corresponding probabilities:
- 0 days: Probability = 0.49
- 1 day: Probability = 0.12
- 2 days: Probability = 0.13
- 3 days: Probability = 0.15
- 4 days: Probability = 0.06
- 5 days: Probability = 0.02
- 6 days: Probability = 0.02
- 7 days: Probability = 0.01
2. Calculate the Expected Value (Mean):
The mean, or expected value, of [tex]$G$[/tex] is calculated using the formula for expected value:
[tex]\[
\text{Mean of } G = \sum (\text{Number of Days} \times \text{Probability})
\][/tex]
Substituting the values from the table, we calculate:
[tex]\[
\begin{align*}
\text{Mean of } G & = (0 \times 0.49) + (1 \times 0.12) + (2 \times 0.13) \\
& \quad + (3 \times 0.15) + (4 \times 0.06) + (5 \times 0.02) \\
& \quad + (6 \times 0.02) + (7 \times 0.01) \\
& = 0 + 0.12 + 0.26 + 0.45 + 0.24 + 0.10 + 0.12 + 0.07 \\
& = 1.36
\end{align*}
\][/tex]
3. Interpretation:
The mean value of 1.36 suggests that, on average, if you randomly select a large number of gym members, they would have worked out about 1.36 days per week.
Therefore, the best interpretation choice based on this mean is:
"If many, many members were randomly selected, the average number of days per week a member worked out would be about 1.36 days."
1. Identify the Number of Days and their Probabilities:
We have the number of days members worked out and their corresponding probabilities:
- 0 days: Probability = 0.49
- 1 day: Probability = 0.12
- 2 days: Probability = 0.13
- 3 days: Probability = 0.15
- 4 days: Probability = 0.06
- 5 days: Probability = 0.02
- 6 days: Probability = 0.02
- 7 days: Probability = 0.01
2. Calculate the Expected Value (Mean):
The mean, or expected value, of [tex]$G$[/tex] is calculated using the formula for expected value:
[tex]\[
\text{Mean of } G = \sum (\text{Number of Days} \times \text{Probability})
\][/tex]
Substituting the values from the table, we calculate:
[tex]\[
\begin{align*}
\text{Mean of } G & = (0 \times 0.49) + (1 \times 0.12) + (2 \times 0.13) \\
& \quad + (3 \times 0.15) + (4 \times 0.06) + (5 \times 0.02) \\
& \quad + (6 \times 0.02) + (7 \times 0.01) \\
& = 0 + 0.12 + 0.26 + 0.45 + 0.24 + 0.10 + 0.12 + 0.07 \\
& = 1.36
\end{align*}
\][/tex]
3. Interpretation:
The mean value of 1.36 suggests that, on average, if you randomly select a large number of gym members, they would have worked out about 1.36 days per week.
Therefore, the best interpretation choice based on this mean is:
"If many, many members were randomly selected, the average number of days per week a member worked out would be about 1.36 days."
Thanks for taking the time to read Your neighborhood gym tracked how many days each of its members worked out over the past week Let tex G tex represent the number of. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
