Suppose we have a binomial experiment in which success is defined to be a partic
ID: 3223449 • Letter: S
Question
Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 43 and p = 0.15. Can we approximate p by a normal distribution? Why? (Use 2 decimal places.) np = nq = be approximated by a normal random variable because What are the values of mu_p and sigma_p? (Use 3 decimal places.) mu_p sigma_p = (b) Suppose n = 25 and p = 0.15. Can we safely approximate p by a normal distribution? Why or why not?, p be approximated by a normal random variable because (c) Suppose n = 42 and p = 0.36. Can we approximate p by a normal distribution? Why? (Use 2 decimal places.) np = nq = be approximated by a normal random variable because What are the values of mu_p and mu_p? (Use 3 decimal places.) mu_p = sigma_p =Explanation / Answer
(A)
n = 43, p = 0.15
np = 0.15 * 43 = 6.45
nq = 0.85 * 43 = 36.55
mu(pcap) = np = 6.45
sigma(pcap) = sqrt(npq) = sqrt(43 * 0.15 * 0.85) = 0.2342
We can approximate pcap by a normal distribution because np and nq are greater than 5.
(B)
for n =25 and p = 0.15
np = 3.75
We can not approximate the value of pcap safely because np < 5 hence we can use the normal approximation here.
(C)
n = 42, p = 0.36
np = 0.36 * 42 = 15.12
nq = 0.64 * 42 = 26.88
mu(pcap) = np = 15.12
sigma(pcap) = sqrt(npq) = sqrt(42 * 0.36 * 0.64) = 3.1108
We can approximate pcap by a normal distribution because np and nq are greater than 5.