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kow [346]
3 years ago
11

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine foun

d in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded a mean nicotine content of 26.2 milligrams and standard deviation of 2.9 milligrams for a sample of n = 95 cigarettes. Estimate the mean nicotine content with a 95% confidence interval.
Mathematics
1 answer:
Alenkasestr [34]3 years ago
4 0

Answer:

The mean nicotine content with a 95% confidence interval is (25.52mg, 26.88mg).

Step-by-step explanation:

The sample size is 95.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

df = 95-1 = 94

Then, we need to subtract one by the confidence level \alpha and divide by 2. So:

\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 94 and 0.025 in the t-distribution table, we have T = 2.28.

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

s = \frac{2.9}{\sqrt{95}} = 0.2975

Now, we multiply T and s

M = T*s = 2.28*0.2975 = 0.6783

For the lower end of the interval, we subtract the mean by M. So 26.2 - 0.6783 = 25.52mg

For the upper end of the interval, we add the mean to M. So 26.2 + 0.6783 = 26.88mg

The mean nicotine content with a 95% confidence interval is (25.52mg, 26.88mg).

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Ok listen here

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We all know that a lot of people think the surface of the earth is ugly, and they have given up hope that people can change it, but the truth is that, the world is beautiful and we can change it.

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4(3x+2y) distributive property pls help
Sonbull [250]

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12x+8y

Step-by-step explanation:

1) Expand by distributing terms.

4*3x+4*2y

2) Simplify 4*3x to 12x.

12x+4*2y

3) Simplify  4*2y to 8y.

12x+8y

<u>Therefor, the answer is </u><u>12x + 8y.</u>

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Let segments AB, BC, and CA be tangent to circle G. If AB=52, BF=20, and CD=21, calculate the perimeter of triangle ABC. The ans
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3. At noon Lan is in his blue mini-van 300 km north of Makenna in her Bugatti. Lan heads south
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Answer:

The rate at which the distance between them is changing at 2:00 p.m. is approximately 1.92 km/h

Step-by-step explanation:

At noon the location of Lan = 300 km north of Makenna

Lan's direction = South

Lan's speed = 60 km/h

Makenna's direction and speed = West at 75 km/h

The distance  Lan has traveled at 2:00 PM = 2 h × 60 km/h = 120 km

The distance north between Lan and Makenna at 2:00 p.m = 300 km - 120 km = 180 km

The distance West Makenna has traveled at 2:00 p.m. = 2 h × 75 km/h = 150 km

Let 's' represent the distance between them, let 'y' represent the Lan's position north of Makenna at 2:00 p.m., and let 'x' represent Makenna's position west from Lan at 2:00 p.m.

By Pythagoras' theorem, we have;

s² = x² + y²

The distance between them at 2:00 p.m. s = √(180² + 150²) = 30·√61

ds²/dt = dx²/dt + dy²/dt

2·s·ds/dt = 2·x·dx/dt + 2·y·dy/dt

2×30·√61 × ds/dt = 2×150×75 + 2×180×(-60) = 900

ds/dt = 900/(2×30·√61) ≈ 1.92

The rate at which the distance between them is changing at 2:00 p.m. ds/dt ≈ 1.92 km/h

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3 years ago
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