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?

Homework Answers

Answer #1

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

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
One hundred draws will be made at random with replacement from the box [1  6  7  9  9  10] a) Find...
One hundred draws will be made at random with replacement from the box [1  6  7  9  9  10] a) Find the expected value and the standard error for the percentage of tickets marked by “9” in 100 draws. Make a box model. b) What is the chance that the percentage of tickets marked by  “9” is less than 40% ? Show work using the normal curve.   
3. Four hundred tickets are drawn at random with replacement from the box [0,0,0,1,2,3] a) What...
3. Four hundred tickets are drawn at random with replacement from the box [0,0,0,1,2,3] a) What is the expected value of the sum of the draws? b) What is the standard error for the sum of the draws? c) What is the probability that the average of the draws is more than 1.075?
900 draws will be made at random with replacement from the box [2 4 6 8]....
900 draws will be made at random with replacement from the box [2 4 6 8]. Estimate the chance that the sum of the draws will be more than 4,600. (Round two decimals)
Consider a box containing the following numbers. 9, 10, 14, 15, 17 The SD for the...
Consider a box containing the following numbers. 9, 10, 14, 15, 17 The SD for the box is 3.03. Suppose 25 draws are made at random with replacement from the box. The expected value for this sum is    The standard error for this sum is    The expected value for the average of the draws is    The standard error for the average of the draws is   
Consider a box containing the following numbers. 3, 5, 10, 14, 17 The SD for the...
Consider a box containing the following numbers. 3, 5, 10, 14, 17 The SD for the box is 5.27. Suppose 100 draws are made at random with replacement from the box. The expected value for the average of the draws is ___ give or take ___ Find the chance that the average of the draws is less than 10.33. ___ Find the chance that the average of the draws is between 9.27 and 10.33. ___
Twenty draws are made with replacement from a standard deck of playing cards. Find the chance...
Twenty draws are made with replacement from a standard deck of playing cards. Find the chance of (1) getting all non-aces (2)not getting all non-aces (3) getting at least one ace. (4) Getting no red ace.
A box contains tickets labeled with the numbers {4, -2, 0, 3, -5}. In 100 random...
A box contains tickets labeled with the numbers {4, -2, 0, 3, -5}. In 100 random draws with replacement from the box, the SE of the sum of just the negative numbers on the tickets drawn is closest to: answer: 10 x 1.959 can someone please show how to get this answer + explain step by step
1. Consider the box: [0,2,3,4,6] a.) If 2 tickets are drawn at random without replacment from...
1. Consider the box: [0,2,3,4,6] a.) If 2 tickets are drawn at random without replacment from this box, what is the probability that the sum of the draws is equal to 6? b.) If 400 tickets are drawn at random with replacment from this box, what is the approximate probability that the average of the draws is between 3.1 and 3.2?
You can draw either 10 times or 100 times at random with replacement from the box...
You can draw either 10 times or 100 times at random with replacement from the box [−1 1]. How many times should you draw? (a) To win $1 when the sum is 5 or more, and nothing otherwise? (b) To win $1 when the sum is −5 or less, and nothing otherwise?    (c) To win $1 when the sum is between −5 and 5, and nothing otherwise?
A large collection of​ one-digit random numbers should have about​ 50% odd and​ 50% even digits\...
A large collection of​ one-digit random numbers should have about​ 50% odd and​ 50% even digits\ because five of the ten digits are odd​ (1, 3,​ 5, 7, and​ 9) and five are even​ (0, 2,​ 4, 6, and​ 8).A. .Find the proportion of​ odd-numbered digits in the following lines from a random number table. Count carefully: 9 9 2 8 9 7 6 5 8 3 0 8 6 0 2 3 7 8 4 9 9 2 8...