83.7k views
0 votes
X is a binomial random variable. (Give your answers correct to three decimal places.)

(a) Calculate the probability of x for: n = 4, x = 2, p = 0.55
P(x) =

(b) Calculate the probability of x for: n = 5, x = 0, p = 0.55
P(x) =

(c) Calculate the probability of x for: n = 7, x = 5, p = 0.55
P(x) =

(d) Calculate the probability of x for: n = 7, x = 3, p = 0.15
P(x) =

(e) Calculate the probability of x for: n = 1, x = 0, p = 0.7
P(x) =

(f) Calculate the probability of x for: n = 9, x = 4, p = 0.2
P(x) =

User Jchristin
by
8.0k points

1 Answer

6 votes

Final answer:

To calculate the probabilities for different values of a binomial random variable X, use the binomial probability formula P(X = x) = C(n, x) * (p^x) * (q^(n-x)) with the given n, x, and p values, performing calculations and rounding to three decimal places.

Step-by-step explanation:

The question at hand deals with calculating probabilities using the binomial distribution. A binomial random variable X represents the number of successes in n independent trials, with each trial having two possible outcomes: success (with probability p) and failure (with probability q, where q=1-p).

To calculate the probability of x successes, we use the binomial probability formula:

P(X = x) = C(n, x) * (p^x) * (q^(n-x)),

where C(n, x) represents the combination of n items taken x at a time.

  1. For n = 4, x = 2, p = 0.55: P(2) = C(4, 2) * (0.55^2) * (0.45^2)
  2. For n = 5, x = 0, p = 0.55: P(0) = C(5, 0) * (0.55^0) * (0.45^5)
  3. For n = 7, x = 5, p = 0.55: P(5) = C(7, 5) * (0.55^5) * (0.45^2)
  4. For n = 7, x = 3, p = 0.15: P(3) = C(7, 3) * (0.15^3) * (0.85^4)
  5. For n = 1, x = 0, p = 0.7: P(0) = C(1, 0) * (0.7^0) * (0.3^1)
  6. For n = 9, x = 4, p = 0.2: P(4) = C(9, 4) * (0.2^4) * (0.8^5)

The calculations must be done using the combination formula and the relevant probability powers, and then the results are rounded to three decimal places.

User David Zech
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.