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Anastasy [175]
3 years ago
5

A new drug on the market is known to cure 24% of patients with colon cancer. If a group of 15 patients is randomly selected, wha

t is the probability of observing, at most, two patients who will be cured of colon cancer? 15 choose 2(0.24)2(0.76)13 15 choose 0(0.76)15 + 15 choose 1(0.24)1(0.76)14 + 15 choose 2(0.24)2(0.76)13 1 − 15 choose 2(0.24)2(0.76)13 15 choose 0 (0.76)15 1 − 15 choose 0 (0.76)15
Mathematics
1 answer:
Zigmanuir [339]3 years ago
4 0

Answer:

P = ₁₅C₀ (0.76)¹⁵ + ₁₅C₁ (0.24)¹ (0.76)¹⁴ + ₁₅C₂ (0.24)² (0.76)¹³

Step-by-step explanation:

Binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

Here, n = 15, p = 0.24, and q = 0.76.

We want to find the probability when r is at most 2, which means r = 0, r = 1, and r = 2.

P = ₁₅C₀ (0.24)⁰ (0.76)¹⁵⁻⁰ + ₁₅C₁ (0.24)¹ (0.76)¹⁵⁻¹ + ₁₅C₂ (0.24)² (0.76)¹⁵⁻²

P = ₁₅C₀ (0.76)¹⁵ + ₁₅C₁ (0.24)¹ (0.76)¹⁴ + ₁₅C₂ (0.24)² (0.76)¹³

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The statistical difference between a process operating at a 5 sigma level and a process operating at a 6 sigma level is markedly
Svet_ta [14]

Answer:

True

Step-by-step explanation:

A six sigma level has a lower and upper specification limits between \\ (\mu - 6\sigma) and \\ (\mu + 6\sigma). It means that the probability of finding no defects in a process is, considering 12 significant figures, for values symmetrically covered for standard deviations from the mean of a normal distribution:

\\ p = F(\mu + 6\sigma) - F(\mu - 6\sigma) = 0.999999998027

For those with defects <em>operating at a 6 sigma level, </em>the probability is:

\\ 1 - p = 1 - 0.999999998027 = 0.000000001973

Similarly, for finding <em>no defects</em> in a 5 sigma level, we have:

\\ p = F(\mu + 5\sigma) - F(\mu - 5\sigma) = 0.999999426697.

The probability of defects is:

\\ 1 - p = 1 - 0.999999426697 = 0.000000573303

Well, the defects present in a six sigma level and a five sigma level are, respectively:

\\ {6\sigma} = 0.000000001973 = 1.973 * 10^{-9} \approx \frac{2}{10^9} \approx \frac{2}{1000000000}

\\ {5\sigma} = 0.000000573303 = 5.73303 * 10^{-7} \approx \frac{6}{10^7} \approx \frac{6}{10000000}  

Then, comparing both fractions, we can confirm that a <em>6 sigma level is markedly different when it comes to the number of defects present:</em>

\\ {6\sigma} \approx \frac{2}{10^9} [1]

\\ {5\sigma} \approx \frac{6}{10^7} = \frac{6}{10^7}*\frac{10^2}{10^2}=\frac{600}{10^9} [2]

Comparing [1] and [2], a six sigma process has <em>2 defects per billion</em> opportunities, whereas a five sigma process has <em>600 defects per billion</em> opportunities.

8 0
3 years ago
Which graph shape represents the polar curve r = 1 + 4sin(θ)?
umka2103 [35]

Answer:

A cardioid

Step-by-step explanation:

A cardioid is a curve in the shape of a heart traced by a point on the circumference of a circle as it rolls around a fixed circle of the same radius.

The equation of vertical cardioid is r=a ± a\sin \theta

Given the polar curve is r= 1+ 4 \sin \theta

This is an equation of vertical cardioid.

So, it represents a cardioid.

7 0
3 years ago
Read 2 more answers
What is 30% of $100?
lord [1]

Answer:

solution. :

30/100*$100

$30

6 0
3 years ago
What is the exact volume of the cylinder with a radius of 13 and a height of 30?
torisob [31]
The volume would be <span>15927.87
so
</span>V ≈ 15927.87to be sure with my answer.
8 0
3 years ago
If m1 =53 what is m3
Thepotemich [5.8K]

Answer:

143

Step-by-step explanation:

90-53=37

180-37=143

5 0
2 years ago
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