Question

# One hundred draws will be made at random with replacement from the box with the following...

One hundred draws will be made at random with replacement from the box with the following numbers: 1 6 7 9 9 10 What is the expected value of a sum of 100 draws from this box?

Using the same box of numbers described above, what is the standard error of a sum of 100 draws from this box?

Using the same box of numbers described above, what is the chance of getting a sum between 650 and 750?

E(Xi) = 1/6 ( 1+ 6 +7 + 9 + 9 +10) = 7

 x p px px^2 1 0.166666667 0.166666667 0.166667 6 0.166666667 1 6 7 0.166666667 1.166666667 8.166667 9 0.333333333 3 27 10 0.166666667 1.666666667 16.66667 1 7 58

Var(Xi) = E(X^2) - E(X) ^2

= 58 - 7^2 = 58 -49 = 9

What is the expected value of a sum of 100 draws from this box?

S = X1+X2+..X100

E(S) = 100 E(X) = 700

Using the same box of numbers described above, what is the standard error of a sum of 100 draws from this box?

Var(S) = 100 * 9 = 900

Using the same box of numbers described above, what is the chance of getting a sum between 650 and 750?

since n= 100 > 30

we can use central limit theorem

Z = (S - 700)/sqrt(900) = (S - 700)/30

P( 650 <S< 750)

= 0.9044