Kiesha's quality-control manager told her she must have [tex]$97\%$[/tex] of her clocks functioning properly. She found a report that said 6 out of 300 clocks tested were not working properly. Kiesha predicts that she will have enough working clocks to please the manager.

Which statements are true about Kiesha's prediction? Select three options.

A. Kiesha's experimental probability is [tex]\frac{1}{30}[/tex].
B. Kiesha will have more than [tex]$97\%$[/tex] of the products working.
C. Kiesha will not meet [tex][tex]$97\%$[/tex][/tex] because more than [tex]$3\%$[/tex] of her clocks will be broken.
D. Kiesha's experimental probability is [tex]\frac{1}{50}[/tex].
E. When the inventory is 4000 clocks, the prediction is that 3920 clocks will work.



Answer :

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.