Assume a binomial probability distribution with n=55 and (pie symbol= .20). Comp

Question

Assume a binomial probability distribution with n=55 and (pie symbol= .20). Compute the following: (Round all z values to 2 decimal places.) a. The mean and standard deviation of the random variable. (Round your "" to 4 decimal places and mean to 1 decimal place.) b. The probability that X is 13 or more. (Use the rounded values found above. Round your answer to 4 decimal places.) Probability c. The probability that X is 9 or less. (Use the rounded values found above. Round your answer to 4 decimal places.) Probability

Explanation / Answer

a.

Mean = n*p = 55*0.20 = 11

Standard deviation = sqrt(n*p*(1-p)) = sqrt(55*0.20*0.80) = 2.9665

b.

Since, n*p and n*(1-p) are greater than 10, we can approximate this Binomial distribution using Normal distribution..

z-score corresponding to 13 = (13-11)/2.9665 = 0.6742

P(x>13) = 1 -P(x<13) = 1 -P (z < 0.6742) = 1 - 0.7450 = 0.250

c)

z-score corresponding to 9 = (9-11)/2.9665 = -0.6742

P(x<9) = P (z < -0.6742) = 0.250.

Note: This can be derived based on symmetry of Normal distribution as well. since mean is 9, P(X>13)=P(x<9)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.