Abinomial 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

Correct: Third option μx = 9 and σx = 2.51

Step-by-step 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

And the variance is

The standard deviation is

The given binomial distribution has the following parameters

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

The standard deviation is

The third option is the correct one

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50