Binomial Experiments: Find Probability of x=5, x>=6, x<4

In summary, the probability that the number of U.S. adults who trust national newspapers to present the news fairly and accurately is at least six is (.37*.6).
  • #1
aprilryan
20
0
Hi all,

I'm a bit confused on this problem in my book.

"Specify the values of n, p, and q and list the possible values of the random variable x.
Sixty percent of U.S. adults trust national newspapers to present the news fairly and accurately. You randomly select nine U.S. adults. Find the probability that the number of U.S. adults who trust national newspapers to present the news fairly and accurately is (a) exactly five, (b) at least six, and (c) less than four."

I have the values.

n=9
p=.63
q=.37
x=5
x is at least six
x<4

Would I have to do them on the calculator using binomial pdf and sum commands or find the mean, standard deviation and variance?

Note: I have been shown to do these types of problems on the calculator using the binomial pdf and sum commands.
 
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  • #2
aprilryan said:
Hi all,

I'm a bit confused on this problem in my book.

"Specify the values of n, p, and q and list the possible values of the random variable x.
Sixty percent of U.S. adults trust national newspapers to present the news fairly and accurately. You randomly select nine U.S. adults. Find the probability that the number of U.S. adults who trust national newspapers to present the news fairly and accurately is (a) exactly five, (b) at least six, and (c) less than four."

I have the values.

n=9
p=.63
q=.37
x=5
x is at least six
x<4

Would I have to do them on the calculator using binomial pdf and sum commands or find the mean, standard deviation and variance?

Note: I have been shown to do these types of problems on the calculator using the binomial pdf and sum commands.

Where does $p = 0.63$ comes from? I would say it should be $p=0.6$ according to the question.
 
  • #3
Yes, it was .60. Thanks, I've got this one figured out!
 

FAQ: Binomial Experiments: Find Probability of x=5, x>=6, x<4

1. What is a binomial experiment?

A binomial experiment is a type of statistical experiment in which there are only two possible outcomes, typically labeled as "success" or "failure". Each trial of the experiment is independent and has the same probability of success, denoted as p. Examples of binomial experiments include coin tosses, where the probability of getting heads is 0.5, and medical trials, where the probability of a successful treatment is known.

2. What is the formula for finding the probability of a specific number of successes in a binomial experiment?

The formula for finding the probability of x successes in a binomial experiment is P(x) = nCx * px * (1-p)n-x, where n is the number of trials and x is the desired number of successes. This formula is also known as the binomial probability formula.

3. How do you find the probability of x=5 in a binomial experiment?

To find the probability of x=5 in a binomial experiment, you will need to know the number of trials (n) and the probability of success (p). Once you have these values, you can plug them into the binomial probability formula, P(x) = nCx * px * (1-p)n-x, where x is the desired number of successes, in this case, 5. Solve the equation to find the probability.

4. What does x>=6 mean in a binomial experiment?

In a binomial experiment, x>=6 means the probability of having 6 or more successes in n trials. This includes 6, 7, 8, and so on, up to the maximum number of trials. This notation is called "greater than or equal to" and is used to indicate a range of values.

5. How do you find the probability of x<4 in a binomial experiment?

To find the probability of x<4 in a binomial experiment, you will need to know the number of trials (n) and the probability of success (p). This notation means the probability of having less than 4 successes in n trials. To find this probability, you can either use the binomial probability formula and add the probabilities of x=0, x=1, x=2, and x=3, or you can use the complement rule and subtract the probability of x=4 or more from 1.

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