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Answer :
To calculate the mean number of days gym members worked out in a week (denoted by [tex]\( G \)[/tex]), we use the concept of expected value in probability. The expected value of a random variable is computed as the sum of the products of each possible value the variable can take and their corresponding probabilities.
Here's how you can calculate it step by step:
1. List the number of days members worked out and their associated probabilities:
- 0 days with probability 0.49
- 1 day with probability 0.12
- 2 days with probability 0.13
- 3 days with probability 0.15
- 4 days with probability 0.06
- 5 days with probability 0.02
- 6 days with probability 0.02
2. Calculate the sum of products of each number of days and its corresponding probability:
- [tex]\( (0 \times 0.49) = 0 \)[/tex]
- [tex]\( (1 \times 0.12) = 0.12 \)[/tex]
- [tex]\( (2 \times 0.13) = 0.26 \)[/tex]
- [tex]\( (3 \times 0.15) = 0.45 \)[/tex]
- [tex]\( (4 \times 0.06) = 0.24 \)[/tex]
- [tex]\( (5 \times 0.02) = 0.10 \)[/tex]
- [tex]\( (6 \times 0.02) = 0.12 \)[/tex]
3. Sum all these individual products to get the mean:
[tex]\[
0 + 0.12 + 0.26 + 0.45 + 0.24 + 0.10 + 0.12 = 1.29
\][/tex]
Thus, the mean number of days a gym member worked out in a week is 1.29 days. This means that if a large number of gym members were randomly selected, the average number of days they worked out per week would be about 1.29 days.
Here's how you can calculate it step by step:
1. List the number of days members worked out and their associated probabilities:
- 0 days with probability 0.49
- 1 day with probability 0.12
- 2 days with probability 0.13
- 3 days with probability 0.15
- 4 days with probability 0.06
- 5 days with probability 0.02
- 6 days with probability 0.02
2. Calculate the sum of products of each number of days and its corresponding probability:
- [tex]\( (0 \times 0.49) = 0 \)[/tex]
- [tex]\( (1 \times 0.12) = 0.12 \)[/tex]
- [tex]\( (2 \times 0.13) = 0.26 \)[/tex]
- [tex]\( (3 \times 0.15) = 0.45 \)[/tex]
- [tex]\( (4 \times 0.06) = 0.24 \)[/tex]
- [tex]\( (5 \times 0.02) = 0.10 \)[/tex]
- [tex]\( (6 \times 0.02) = 0.12 \)[/tex]
3. Sum all these individual products to get the mean:
[tex]\[
0 + 0.12 + 0.26 + 0.45 + 0.24 + 0.10 + 0.12 = 1.29
\][/tex]
Thus, the mean number of days a gym member worked out in a week is 1.29 days. This means that if a large number of gym members were randomly selected, the average number of days they worked out per week would be about 1.29 days.
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