Question

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?

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

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 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]. 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 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 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 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 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 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 [−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\ 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...

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