X 1, X 2,...X9 Is a random sample extracted from the infinite population and is

Question

X 1, X 2,...X9 Is a random sample extracted from the infinite population and is set to Xi ~ N (3, 25) for all i = 1, 2, to 9. Define X as mean of Xi (with n = 9). At this time, answer the following questions. ? Find the average of X. Find the variance of X. ? Find P (X <0). ? Find what x in P (X> x) = 0.1. X 1, X 2,...X9 Is a random sample extracted from the infinite population and is set to Xi ~ N (3, 25) for all i = 1, 2, to 9. Define X as mean of Xi (with n = 9). At this time, answer the following questions. ? Find the average of X. Find the variance of X. ? Find P (X <0). ? Find what x in P (X> x) = 0.1. Xi (with n = 9). At this time, answer the following questions. ? Find the average of X. Find the variance of X. ? Find P (X <0). ? Find what x in P (X> x) = 0.1.

Explanation / Answer

Mean of the sample denoted as X,

The mean of Sample(X) is distributed as = N(3, 25/9)

Average of X is the mean value of X= 3

Variance of X = 25/9 = 2.7777

P(X<0) = P( Z< (0-3)/2.7777) = P(Z< =-1.08) = 0.1401

x for which P(X> x) =0.1

P(Z > (x-3)/2.7777) = 1- P(Z< (x-3)/2.777)=0.1

P(Z < (x-3)/2.7777) = 0.9

From z table :

(x -3 )/2.777 = 1.285

x = 6.56944

Related Questions

Navigate

• Browse (All)
• Browse X
• Subjects

---

---

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