Question

A binomial event has n = 30 trials. The probability of success for each trial is 0.30. Let x be the number of successes of the event during the 30 trials. What are μx and σx?

μx = 2.51 and σx = 9
μx = 21 and σx = 6.3
μx = 9 and σx = 2.51
μx = 6.3 and σx = 21

Answer 1

Correct: Third option μx = 9 and σx = 2.51

Explanation:

Binomial Distribution

Being p the probability of success of an individual event, q the probability of failure (q=1-p) and n the number of independent trials of that event, the expected value or mean of the distribution is

`\mu_x=np`

And the variance is

`\sigma_x ^2=npq`

The standard deviation is

`\sigma_x=√(npq)`

The given binomial distribution has the following parameters

n = 30, p = 0.3, q = 1 - 0.3 = 0.7. The mean is

`\mu_x=(30)(0.3)=9`

The standard deviation is

`\sigma_x=√((30)(0.3)(0.7))=√(6.3)`

`\sigma_x=2.51`

The third option is the correct one