c. Find P(x > 2). Interpret this result.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
I was wondering how to solve for Part C? Thanks! The question asks about contaminated gun cartridges for p(x is greater than or equal to 2)
![### Contaminated Gun Cartridges
A weapons manufacturer uses a liquid propellant to produce gun cartridges. During the manufacturing process, the propellant can get mixed with another liquid to produce a contaminated cartridge. A University of South Florida statistician hired by the company to investigate the level of contamination in the stored cartridges found that 23% of the cartridges in a particular lot were contaminated.
Suppose you randomly sample (without replacement) gun cartridges from this lot until you find a contaminated one. Let \( x \) be the number of cartridges sampled until a contaminated one is found. It is known that the probability distribution for \( x \) is given by the formula:
\[
p(x) = (0.23)(0.77)^{x-1}, \quad x = 1, 2, 3, \ldots
\]
**Tasks:**
a. **Find \( p(1) \). Interpret this result.**
b. **Find \( p(5) \). Interpret this result.**
c. **Find \( P(x \geq 2) \). Interpret this result.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54d2e198-bc66-47c9-817f-3561527d5271%2F1ddd844f-789b-4113-a766-63e1d0e5144a%2Fgyvl73o_processed.jpeg&w=3840&q=75)
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