Find the mean and standard deviation of the number of

Tolnaio

Tolnaio

Answered question

2021-09-16

Find the mean and standard deviation of the number of success.

Answer & Explanation

Gennenzip

Gennenzip

Skilled2021-09-17Added 96 answers

Calculation:
It is given that a random experiment has 50 independent trials with success probability of 0.30.
Binomial distribution:
A random variable X is said to follow binomial distribution if the probability mass function of X is,
p(x)=nCxpx(1p)nx,x=0,1,2,,n., with mean np and variance np(1p).
Characteristics of Binomial distribution:
- The number of trials in Binomial distribution is fixed and independent to each other.
- There are only two outcomes, such that, success and failure.
- The probability of success for each trial is constant.
- The random variable is the number of success among total number of trials.
The experiment has 50 independent trials. Moreover this is a random experiment. Hence, all the trials are independent to each other.
In this random experiment there can only be tow outcomes; success and failure.
It is given that the success probability is 0.30 and the experiment is repeated 50 times. Hence, the success probability is same for each trial.
The random variable defines the number of success in the given experiment.
Hence, it is best to use Binomial probability distribution to find the probability.
The mean of the binomial distribution is np.
Hence, the mean of the given distribution is,
np=(50)(0.30)
=15
Thus, the mean is 15.
The variance of the binomial distribution is np(1p).
Thus, the standard deviation of the binomial distribution is np(1p).
Hence, the standard deviation of the given distribution is,
np(1p)=(50)(0.30)(10.30)
=(50)(0.30)(0.70)
=10.5
=3.24
Therefore, the standard deviation is 3.24.

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