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2 months ago

Exhibit: Department Store.

1 answer:

7 0

In detail: Based on the central limit theorem, the distribution appears normal due to the large sample size. The confidence interval is presented in the format: (Sample mean - margin of error, sample mean + margin of error). The sample mean, denoted as x, serves as the point estimate for the population mean. The confidence interval is computed as: mean ± z × σ/√n, where σ represents the population standard deviation. The formula transforms into confidence interval = x ± z × σ/√n, with specific values: x = $75, σ = $24. To find the z score, we subtract the confidence level from 100% which gives α as 1 - 0.96 = 0.04; halving this results in α/2 = 0.02, signifying the tail areas. To ensure we account for the center area, we have 1 - 0.02 = 0.98, corresponding to a z score of 2.05 for the 96% confidence level. The confidence interval becomes 75 ± 2.05 × 24/√64 = 75 ± 2.05 × 3 = 75 ± 6.15. The lower limit is 75 - 6.15 = 68.85, while the upper limit stands at 75 + 6.15 = 81.15. For n = 400, with x = $75 and σ = $24, the z score remains 2.05, resulting in the confidence interval calculated as 75 ± 2.05 × 24/√400 = 75 ± 2.05 × 1.2 = 75 ± 2.46. Subsequently, the lower bound becomes 75 - 2.46 = 72.54, and the upper limit adds up to 75 + 2.46 = 77.46. Lastly, when n = 400, x = $200, and σ = $80, the z score tied to a 94% confidence level is 1.88. Thus, the confidence interval is expressed as 200 ± 1.88 × 80/√400 = 200 ± 1.88 × 4 = 200 ± 7.52, giving us a margin of error of 7.52.

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Triangle L M N is cut by line segment O P. Line segment O P goes from side M L to side M N. The length of O L is 14, the length

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Consider the system: y = 3x + 5 y = ax + b What values for a and b make the system inconsistent? What values for a and b make th

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The Community Relief Fund receives a large donation of $2800. The foundation agrees to spend the money on $20 school bags, $25 s

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The question appears incomplete:

The Community Relief Fund has accepted a significant donation of $2800. The foundation intends to allocate funds for $20 school bags, $25 sweaters, and $5 books. They aim to procure 200 items to send to schools in areas impacted by earthquakes. They must order the same amount of books as the total number of school bags and sweaters combined. How many of each item should they procure?

Answer:

They need to procure 40 bags, 60 sweaters, and 100 books.

Step-by-step explanation:

Based on the information given, we can derive the following equations:

x+y+z=200 (1)

20x+25y+5z=2800 (2)

z=x+y (3), where:

x=amount of bags

y=amount of sweaters

z=amount of books

Now, substituting (3) in (1) and (2):

x+y+x+y=200

2x+2y=200 (4)

20x+25y+5(x+y)=2800

20x+25y+5x+5y=2800

25x+30y=2800 (5)

We obtain 2 equations:

2x+2y=200 (4)

25x+30y=2800 (5)

We can isolate x in (4):

2x=200-2y

x=100-y (6)

Next, we can plug (6) into (5):

25(100-y)+30y=2800

2500-25y+30y=2800

5y=2800-2500

y=300/5

y=60

Now, we can substitute the value of y in (6) to find x:

x=100-60

x=40

Finally, we can replace the values of x and y in (3) to find z:

z=40+60

z=100

Thus, it is concluded that they need to order 40 bags, 60 sweaters, and 100 books.

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