STATS HOMEWORK SHOW YOUR WORK AND EXCEL FUNCTIONS PLEASE! Part ONE: One state lo

Question

STATS HOMEWORK SHOW YOUR WORK AND EXCEL FUNCTIONS PLEASE!

Part ONE:

One state lottery has 1,000 prizes of $1; 120 prizes of $10; 15 prizes of $55; 5 prizes of $280; 2 prizes of $1,200; and 1 prize of $2,300. Assume that 32,000 lottery tickets are issued and sold for $1.

Question 1: what is the lottery's expected profit per ticket?

Question 2: what is the lottery's standard deviation of profit per ticket?

PART TWO:

According to the centers for disease control and prevention, heart disease causes 35% of deaths in the United States. Suppose a sample of 13 recently deceased from across the U.S. were examined for cause of death.

Question 4: Find the probability that between 6 and 11, of the recently deceased died due to heart disease.

Question 5: Find the probability that less than 4 of the recently deceased dies due to heart disease.

PART 3

Gallup Poll showed that 36% Americans are satisfied with the way things are going in the United States. Suppose samples of 25 Americans are selected. Based on this information, generate a cumulative binomial probability distribution in the given space on the satisfied sheet in the workbook to answer the following questions.

Excel table set up: please fill in formatted to 4 decimal places

Question 5: Find the probability that a greater than 4 Americans are satisfied with the way this are going.

Question 6: Find the probability that the number of Americans who are satisfied with the way things are going differs by greater than 1 from the mean.

Questions 7: Find the probability that no more than 6 Americans are satisfies with the way things are going.

Question 8: Find the probability that exactly 14 Americans are not satisfied with the way things are going.

Question 9: Find the probability that more than 30% but most of 70% of these Americans are satisfied with the way things are going.

Question 10. Find the Probability that no less than 15 Americans are satisfied with the way things are going.

Question 11: Find the probability that at least 11 Americans are not satisfied with the way things are going.

a b c 9 Binomial 10 n 11 p 12 13 xi P(X<=xi) 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 138 Note: Answer questions 1 4 by Using your Calk ulate v all decimals uentil yweac yOr nw eound to four One state lottery has 1,000prizes of $1: 120 prizes of $10, 15 prizes of S55, 5 praes of 520,2 pries of S1,200, and 1 prize of $2,300. Assume hor 32,um lottery tickets ar@isuaed and soldforS1. Recording to the Centers for Dissaze Control and Prewention, Feart diseoza ca deceased from across thU.S. wers amines for cause of daath Questions eal butput

Explanation / Answer

part TWO
4.
Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
P( X = 6 ) = ( 13 6 ) * ( 0.35^6) * ( 1 - 0.35 )^7
= 0.1546
P( X = 11 ) = ( 13 11 ) * ( 0.35^11) * ( 1 - 0.35 )^2
= 0.0003
the probability that between 6 and 11, of the recently deceased died due to heart disease is p(x=11)-p(x=6)=0.1543
5.
the probability that less than 4 of the recently deceased dies due to heart disease

P( X < 4) = P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 13 3 ) * 0.35^3 * ( 1- 0.35 ) ^10 + ( 13 2 ) * 0.35^2 * ( 1- 0.35 ) ^11 + ( 13 1 ) * 0.35^1 * ( 1- 0.35 ) ^12 + ( 13 0 ) * 0.35^0 * ( 1- 0.35 ) ^13   
= 0.2783

PART THREE
5.
the probability that a greater than 4 Americans are satisfied with the way this are going
  
P( X < = 4) = P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 25 4 ) * 0.36^4 * ( 1- 0.36 ) ^21 + ( 25 3 ) * 0.36^3 * ( 1- 0.36 ) ^22 + ( 25 2 ) * 0.36^2 * ( 1- 0.36 ) ^23 + ( 25 1 ) * 0.36^1 * ( 1- 0.36 ) ^24 + ( 25 0 ) * 0.36^0 * ( 1- 0.36 ) ^25
= 0.0255

P( X > 4) = 1 - P ( X <=4) = 1 -0.0255 = 0.9745
6.
the probability that the number of Americans who are satisfied with the way things are going differs by greater than 1 from the mean
  
P( X < = 1) = P(X=1) + P(X=0)
= ( 25 1 ) * 0.36^1 * ( 1- 0.36 ) ^24 + ( 25 0 ) * 0.36^0 * ( 1- 0.36 ) ^25
= 0.0002

P( X > 1) = 1 - P ( X <=1) = 1 -0.0002 = 0.9998
7.
the probability that no more than 6 Americans are satisfies with the way things are going
  
P( X < 6) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= ( 25 5 ) * 0.36^5 * ( 1- 0.36 ) ^20 + ( 25 4 ) * 0.36^4 * ( 1- 0.36 ) ^21 + ( 25 3 ) * 0.36^3 * ( 1- 0.36 ) ^22 + ( 25 2 ) * 0.36^2 * ( 1- 0.36 ) ^23 + ( 25 1 ) * 0.36^1 * ( 1- 0.36 ) ^24 + ( 25 0 ) * 0.36^0 * ( 1- 0.36 ) ^25
= 0.0682

8.

P( X = 14 ) = ( 25 14 ) * ( 0.36^14) * ( 1 - 0.36 )^11
= 0.0202

the probability that exactly 14 Americans are not satisfied with the way things are going
= 1-p(x=14)
= 1-0.0202=0.9798
10.
the Probability that no less than 15 Americans are satisfied with the way things are going
  
P( X < = 15) = P(X=15) + P(X=14) + P(X=13) + P(X=12) + P(X=11) + P(X=10) + P(X=9) + P(X=8) + P(X=7) + P(X=6) + P(X=5)   
= ( 25 15 ) * 0.36^15 * ( 1- 0.36 ) ^10 + ( 25 14 ) * 0.36^14 * ( 1- 0.36 ) ^11 + ( 25 13 ) * 0.36^13 * ( 1- 0.36 ) ^12 + ( 25 12 ) * 0.36^12 * ( 1- 0.36 ) ^13 + ( 25 11 ) * 0.36^11 * ( 1- 0.36 ) ^14 + ( 25 10 ) * 0.36^10 * ( 1- 0.36 ) ^15 + ( 25 9 ) * 0.36^9 * ( 1- 0.36 ) ^16 + ( 25 8 ) * 0.36^8 * ( 1- 0.36 ) ^17 + ( 25 7 ) * 0.36^7 * ( 1- 0.36 ) ^18 + ( 25 6 ) * 0.36^6 * ( 1- 0.36 ) ^19 + ( 25 5 ) * 0.36^5 * ( 1- 0.36 ) ^20
= 0.9959

P( X > 15) = 1 - P ( X <=15) = 1 -0.9959 = 0.0041

11.
the probability that at least 11 Americans are not satisfied with the way things are going

P( X < = 11) = P(X=11) + P(X=10) + P(X=9) + P(X=8) + P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1)   
= ( 25 11 ) * 0.36^11 * ( 1- 0.36 ) ^14 + ( 25 10 ) * 0.36^10 * ( 1- 0.36 ) ^15 + ( 25 9 ) * 0.36^9 * ( 1- 0.36 ) ^16 + ( 25 8 ) * 0.36^8 * ( 1- 0.36 ) ^17 + ( 25 7 ) * 0.36^7 * ( 1- 0.36 ) ^18 + ( 25 6 ) * 0.36^6 * ( 1- 0.36 ) ^19 + ( 25 5 ) * 0.36^5 * ( 1- 0.36 ) ^20 + ( 25 4 ) * 0.36^4 * ( 1- 0.36 ) ^21 + ( 25 3 ) * 0.36^3 * ( 1- 0.36 ) ^22 + ( 25 2 ) * 0.36^2 * ( 1- 0.36 ) ^23 + ( 25 1 ) * 0.36^1 * ( 1- 0.36 ) ^24
= 0.851

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