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.

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.