Question

compute p(x) using the binomial probability formula. then determine whether the normal distribution can be used to estimate this probability. if so, p(x) using the normal distribution and compare the result with the exact probability.

n=78, p= 0.83, and x=60

for n= 78, p= 0.83, and x=60, find P(x) using the binomial probability distribution.

P(x) _. (round to four decimal places as needed.)

can the normal distribution be used to approximate this probability?

A. no, the normal distribution cannot be used because np(1-p) < 10.

B. yes, the normal distribution can be used because np(1-p) ≤ 10.

C. yes, the normal distribution can be used because np(1-p) ≥ 10.

D. no, the normal distribution cannot be used because np(1-p) ≥ 10.

Approximate P(x) using the normal distribution. select the correct choice below and fill in any answer boxes in your choice.

A. P(x) = _. (round to four decimal places as needed.)

B. the normal distribution cannot be used to approximate the binomial distribution in this case.

Compare the normal approximation with the exact probability. select the correct choice below and fill in any answer boxes in your choices

A. the exact probability is less than the approximated probability by _.

B. the exact probability is greater than the approximated probability by _.

C. the exact and approximated probabilities are equal

D. the normal distribution cannot be used to approximate the binomial distribution in this case.

Answer 1

Here n=78, p= 0.83, and x=60

So

C. yes, the normal distribution can be used because np(1-p) ≥ 10.

Now mean is np=np=78*0.83=64.74 and standard deviation is sqrt(npq)=3.3175

So Now

B. the exact probability is greater than the approximated probability by 0.0015