Binomial probability distributions depend on the number of trials n of a binomial experiment and the probability of success p on each trial. Under what conditions is it appropriate to use a normal approximation to the binomial? (Select all that apply.)
np > 5
p < 0.5
p > 0.5
nq > 5
np > 10
nq > 10

Correct options: np > 10, nq > 10 and p < 0.50.

Step-by-step explanation:

Let X be discrete binomial random variable.

The probability of success is p and the number of independent trials is n.

The probability mass function of a Binomial distribution is:

In case, the sample size is too large, i.e. n > 30 and the probability of success is too small, i.e. p < 0.50, then the Normal distribution can be used to approximate the Binomial distribution.

The conditions to be satisfied for Normal approximation are:

Thus, the correct options are np > 10, nq > 10 and p < 0.50.

c

step-by-step explanation:

there is vertical asymptote at x = 2 and x = 0

vertical asymptote occurs at the points where the denominator is 0. so we can say that

x = 2 occurs when there is a factor (x-2) in the denominator, and

x = 0 occurs when there is a factor "x" in the denominator

thus, the denominator of the equation would have "x * (x-2)", this is option c only. that's the correct answer.