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Sagot :
Let's solve this problem step by step.
1. Experimental Probability of a Non-Working Clock:
- Kiesha found that 6 out of 300 clocks tested were not working properly.
- The experimental probability that a clock is not working is calculated as:
[tex]\[ \text{Experimental Probability} = \frac{\text{Number of Non-Working Clocks}}{\text{Total Number of Clocks Tested}} = \frac{6}{300} = \frac{1}{50} \][/tex]
- Therefore, Kiesha's experimental probability is [tex]\(\frac{1}{50}\)[/tex].
2. Percentage of Working Clocks:
- If 6 out of 300 clocks are not working, then 294 out of 300 clocks are working.
- The percentage of working clocks is:
[tex]\[ \text{Percentage Working} = \left(1 - \frac{1}{50}\right) \times 100 = \left(1 - 0.02\right) \times 100 = 98\% \][/tex]
- Thus, Kiesha will have more than [tex]\(97 \%\)[/tex] of the products working.
3. Compare to Manager's Requirement:
- Kiesha's manager requires that at least [tex]\(97 \%\)[/tex] of the clocks are working.
- Since Kiesha's percentage of working clocks is [tex]\(98 \%\)[/tex], this is more than the [tex]\(97 \%\)[/tex] requirement.
4. Expected Working Clocks in the Inventory:
- Kiesha's total inventory is 4000 clocks.
- The expected number of working clocks can be calculated as:
[tex]\[ \text{Expected Working Clocks} = \left(\frac{\text{Percentage Working}}{100}\right) \times \text{Total Inventory} = \left(\frac{98}{100}\right) \times 4000 = 3920 \][/tex]
- So, when the inventory is 4000 clocks, the prediction is that 3920 clocks will work.
5. Statements Checking:
- Statement 1: "Kiesha's experimental probability is [tex]\(\frac{1}{30}\)[/tex]": False. It is actually [tex]\(\frac{1}{50}\)[/tex].
- Statement 2: "Kiesha will have more than [tex]\(97 \%\)[/tex] of the products working": True. She will have [tex]\(98 \%\)[/tex] working products.
- Statement 3: "Kiesha will not meet [tex]\(97 \%\)[/tex] because more than [tex]\(3 \%\)[/tex] of her clocks will be broken": False. Less than [tex]\(3 \%\)[/tex] (i.e., [tex]\(2 \%\)[/tex]) of her clocks will be broken.
- Statement 4: "Kiesha's experimental probability is [tex]\(\frac{1}{50}\)[/tex]": True.
- Statement 5: "When the inventory is 4000 clocks, the prediction is that 3920 clocks will work": True.
Correct Statements:
- Kiesha will have more than [tex]$97 \%$[/tex] of the products working.
- Kiesha's experimental probability is [tex]$\frac{1}{50}$[/tex].
- When the inventory is 4000 clocks, the prediction is that 3920 clocks will work.
1. Experimental Probability of a Non-Working Clock:
- Kiesha found that 6 out of 300 clocks tested were not working properly.
- The experimental probability that a clock is not working is calculated as:
[tex]\[ \text{Experimental Probability} = \frac{\text{Number of Non-Working Clocks}}{\text{Total Number of Clocks Tested}} = \frac{6}{300} = \frac{1}{50} \][/tex]
- Therefore, Kiesha's experimental probability is [tex]\(\frac{1}{50}\)[/tex].
2. Percentage of Working Clocks:
- If 6 out of 300 clocks are not working, then 294 out of 300 clocks are working.
- The percentage of working clocks is:
[tex]\[ \text{Percentage Working} = \left(1 - \frac{1}{50}\right) \times 100 = \left(1 - 0.02\right) \times 100 = 98\% \][/tex]
- Thus, Kiesha will have more than [tex]\(97 \%\)[/tex] of the products working.
3. Compare to Manager's Requirement:
- Kiesha's manager requires that at least [tex]\(97 \%\)[/tex] of the clocks are working.
- Since Kiesha's percentage of working clocks is [tex]\(98 \%\)[/tex], this is more than the [tex]\(97 \%\)[/tex] requirement.
4. Expected Working Clocks in the Inventory:
- Kiesha's total inventory is 4000 clocks.
- The expected number of working clocks can be calculated as:
[tex]\[ \text{Expected Working Clocks} = \left(\frac{\text{Percentage Working}}{100}\right) \times \text{Total Inventory} = \left(\frac{98}{100}\right) \times 4000 = 3920 \][/tex]
- So, when the inventory is 4000 clocks, the prediction is that 3920 clocks will work.
5. Statements Checking:
- Statement 1: "Kiesha's experimental probability is [tex]\(\frac{1}{30}\)[/tex]": False. It is actually [tex]\(\frac{1}{50}\)[/tex].
- Statement 2: "Kiesha will have more than [tex]\(97 \%\)[/tex] of the products working": True. She will have [tex]\(98 \%\)[/tex] working products.
- Statement 3: "Kiesha will not meet [tex]\(97 \%\)[/tex] because more than [tex]\(3 \%\)[/tex] of her clocks will be broken": False. Less than [tex]\(3 \%\)[/tex] (i.e., [tex]\(2 \%\)[/tex]) of her clocks will be broken.
- Statement 4: "Kiesha's experimental probability is [tex]\(\frac{1}{50}\)[/tex]": True.
- Statement 5: "When the inventory is 4000 clocks, the prediction is that 3920 clocks will work": True.
Correct Statements:
- Kiesha will have more than [tex]$97 \%$[/tex] of the products working.
- Kiesha's experimental probability is [tex]$\frac{1}{50}$[/tex].
- When the inventory is 4000 clocks, the prediction is that 3920 clocks will work.
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