Assume the random variable X has a binomial distribution with

Yasmin 2021-10-02 Answered

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success . Round your answer to four decimal places. \(\displaystyle{P}{\left({X}{<}{4}\right)},{n}={6},{p}={0.4}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Bella
Answered 2021-10-03 Author has 6226 answers

Step 1
The Binomial probability distribution is:
In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.
Step 2
The value of \(\displaystyle{P}{\left({X}{<}{4}\right)}\) is,
\(\displaystyle{P}{\left({X}{<}{4}\right)}={P}{\left({X}={0}\right)}+{P}{\left({X}={1}\right)}+{P}{\left({X}={2}\right)}+{P}{\left({X}={3}\right)}\)
\(=\left(\begin{array}{c}6\\ 0\end{array}\right)(0.4)^{0}(1-0.4)^{6-0}+\left(\begin{array}{c}6\\ 0\end{array}\right)(0.4)^{1}(1-0.4)^{6-1}+\left(\begin{array}{c}6\\ 2\end{array}\right)(0.4)^{2}(1-0.4)^{6-2}+\left(\begin{array}{c}6\\ 3\end{array}\right)(0.4)^{3}(1-0.4)^{6-3}\)
\(\displaystyle={0.0467}+{0.1866}+{0.3110}+{0.2765}\)
\(\displaystyle={0.8208}\)
Thus, the value of \(\displaystyle{P}{\left({X}{<}{4}\right)}\) is 0.8208.

Have a similar question?
Ask An Expert
42
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-28
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. \(\displaystyle{P}{\left({X}={14}\right)},{n}={16},{p}={0.8}\)
asked 2021-08-30
A binomial random variable has mean 1.8 and variance 1.44. Determine complete binomial probability distribution.
asked 2021-08-18
Explain how the value of n, the number of trials in a binomial experiment, affects the shape of the distribution of a binomial random variable.
asked 2021-09-17
Assume a binomial probability distribution has \(\displaystyle{p}={.60}\ {\quad\text{and}\quad}\ {n}={200}\).
a. what are the mean and standard deviation?
b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.
c. what is the probability of 100 to 110 successes?
asked 2021-09-07
Assume a binomial probability distribution has p = 0.80 and n = 400.
a) what is the mean and standard deviation
b) is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.
c) what is the probability of 300 to 310 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)
asked 2021-10-01

X denotes a binomial random variable with parameters n and p, Indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.
\(\displaystyle{P}{\left({X}{<}{4}\right)}\)

asked 2021-09-29

X denotes a binomial random variable with parameters n and p. For each exercise, indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.
\(\displaystyle{P}{\left({7}{<}{X}{<}{10}\right)}\)

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question
...