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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

Respuesta :

Answer:

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:

[tex]P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...[/tex]

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:

  • [tex]np>10\\[/tex]
  • [tex]n(1-p)>10[/tex]

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