Question

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)

Answer #1

x | P(X=x) | xP(x) |
x^{2}P(x) |

2 | 0.250 | 0.50000 | 1.00000 |

4 | 0.250 | 1.00000 | 4.00000 |

6 | 0.250 | 1.50000 | 9.00000 |

8 | 0.250 | 2.00000 | 16.00000 |

total | 5.0000 | 30.0000 | |

E(x) =μ= | ΣxP(x) = | 5.0000 | |

E(x^{2}) = |
Σx^{2}P(x) = |
30.0000 | |

Var(x)=σ^{2} = |
E(x^{2})-(E(x))^{2}= |
5.0000 | |

std deviation= |
σ= √σ^{2} = |
2.2361 |

expected sum of 900 draws =900*5 =4500

and standard deviation =2.2361*√900 =67.082

from normal approximation:

chance that the sum of the draws will be more than 4,600 :

P(X>4600)=P(Z>(4600-4500)/67.082)=P(Z>1.49)=**0.07**

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?

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?

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

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. ___

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?

Two numbers are selected at random and with replacement from the
set {1, 2, 3, 4, 5, 6}.
What is the probability that the first one is equal to the
second?
What is the probability that the first one is greater than the
second?

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 person draws 3 cards without replacement from a standard
52-card deck. Find the probability of drawing exactly two 4 , 5 ,6
, or 7s.

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