Question

8Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(x) using the normal distribution and compare the result with the exact probability. na 72. p-o.77, and x-56 Cli Cli e (page 1).1 page 2).2 For n-72, p-0.77, and x-56, find P(x) using the binomial probability distribution. P(x)- Can the normal distribution be used to approximate this probability? Round to four decimal places as needed.) O A. Yes, the normal distribution can be used because np(1-p)s 10. OB. No, the normal distribution cannot be used because np(1 p)210 OC. No, the normal distribution cannot be used because np(1 -p)10 O D. Yes, the normal distribution can be used because np(1-p)2 10 Approximate P(x) using the normal distribution. Select the correct choice below and fill in any answer boxes in your choice OA. P(x) O B. The normal distribution cannot be used to approximate the binomial distribution in this case. (Round to four decimalplaces as needed.) Compare the normal approximation with the exact probability. Select the correct choice below and fill in any answer boxes in your choice O A. The exact probability is greater than the approximated probability by OB. The exact probability is less than the approximated probability by (Round to four decimal places as needed.) (Round to four decimal places as needed.) C. OD. The exact and approximated probabilities are equal. The normal distribution cannot be used to approximate the binomial distribution in this case.

Answer 1

Here, x = 56
P(x =56) = 72C56 * 0.77^56 *(1-0.77)^16
= 0.1111

yes because normal distribution can be used because np(1-p)>=10

P(x = 56)
using continuity correction

mean = np = 72*0.77 = 55.44
std.dev = sqrt(npq)
= sqrt(72*0.77*0.23)
= 3.5709

P(x = 56)
= P(x - 0.5 < x < x+0.5)
= P(55.5 < x < 56.5)
= P((55.5 - 55.44)/3.5709 < z < (56.5 - 55.44)/3.5709)
= P(0.0168 <z < 0.2968)
= 0.1100

The exact probability is gretaer than teh approximated by 0.0011