A simple random sample of 10 students is selected, with replacement, from a larg

Question

A simple random sample of 10 students is selected, with replacement, from a large group of UL Lafayette students. If 80% of the students in this group were born in Louisiana, find the probability of the following events.

a) All ten of the students were born in Louisiana.

b) The first student chosen for the sample and the fifth student chosen for the sample were not born in Louisiana but the other eight were.

c) Two of the ten students were not born in Louisiana but the other eight were.

d) The seventh student selected for the sample was born in Louisiana.

e) Use the appropriate formulas attached for the binomial distribution as applicable here, to find the expected value and variance of X, where X denotes the number of the ten students selected who were born in Louisiana. (formulas attached above)

PLEASE EXPLAIN and show work for EVERY QUESTION with the answer !

The binomial distribution with parameters n (number of trials) and p (success probability). Restrictions on the parameters: n is a positive integer (1,2,3, and 0

Explanation / Answer

A simple random sample of 10 students is selected, with replacement, from a large group of UL Lafayette students. If 80% of the students in this group were born in Louisiana, find the probability of the following events.

a) All ten of the students were born in Louisiana.

Here n = 10 and p = 0.8

from the above given formula in the question

Pr( X = 10) = 10C 10 (0.8)10 (0.2)0 = 0.1074

b) The first student chosen for the sample and the fifth student chosen for the sample were not born in Louisiana but the other eight were.

ANswer : First and fifth student is not from louisiana and rest are from louisiana

P(1st and 5th not from louisiana) = (0.2)2 (0.8) 8 = 0.0067

c) Two of the ten students were not born in Louisiana but the other eight were.

P ( X =2) = 10C8 (0.8)8 (0.2)2 = 0.3020

d) The seventh student selected for the sample was born in Louisiana.

P(7th is from louisinia) = 0.8 (as events are independent)

e) Use the appropriate formulas attached for the binomial distribution as applicable here, to find the expected value and variance of X, where X denotes the number of the ten students selected who were born in Louisiana. (formulas attached above)

Expected Value = np = 10 * 0.8 = 8.0

Variance (X) = np(1-p) = 10 * 0.8 * 0.2 = 1.6

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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