Swaziland has the highest HIV prevalence in the world: 25.9% of this country’s population is infected with HIV. The ELISA test is one of the first and most accurate tests for HIV. For those who carry HIV, the ELISA test is 99.7% accurate. For those who do not carry HIV, the test is 92.6% accurate. If an individual from Swaziland has tested positive, what is the probability that they carry HIV

Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 7.3 percent and the standard deviation was 8.4 percent. What is the probability that your return on this asset will be less than –4.5 percent in a given year? Use the NORMDIST function in Excel® to answer this question. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Probability 8.0 % What range of returns would you expect to see 95 percent of the time? (Enter your answers for the range from lowest to highest. Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) 95% level % to % What range would you expect to see 99 percent of the time? (Enter your answers for the range from lowest to highest. Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded

Three digits are randomly chosen from {1,2,3,4,5,6,7} without replacement.

a) What is the probability the number formed is 123 or 567?

b) What is the probability the number formed has first digit 1?

c) What is the probability the number formed by the three digits is greater than 520?

A 79-kg person stands on a bathroom scale and rides in an elevator whose vy-versus-time graph is shown in Figure 1

a. What is the reading on the scale at t=1.0s?

b. What is the reading on the scale at t=4.0s?

c. What is the reading on the scale at t=8.0s?

The waiting time for a patient at doctor cholocks office is normally distributed with mean of 15 minutes and standard deviation 4.3. The waiting time for a patient at doctor Kaur’s office is normally distributed with mean 12 minutes and standard deviation 1.5

1. Which doctor should you choose in order to have the highest probability of seeing the doctor in less than 10 minutes. Find these probabilities.
2. What is the third quartile in waiting times of Doctor cholock patients?
3. If four of Doctor Kaur’s patients are selected at random what is the probability that their average waiting time is within 2 minutes of the mean.

Scenario: There is a box containing 4 different type color of balls green, blue, white and black there are total 20 balls in the box the number of different colored balls are given below: green - only 1 ball blue - 4 balls white - 8 balls black - 7 balls If you want to get a chance to select a ball from the box you must pay $2 and it will not get back if you win or loss. Each ball color wins different type of amount. The amount that are given to the player if he selects

green =$20 blue =$3 white =$1 black =$0

Would you play the game if; Probability of getting green ball=1/20

Probability of getting blue ball =4/20

Probability of getting white ball =8/20

Probability of getting black ball =7/20

Change that comes into our amount after selecting a ball is given if Select a green ball = $20-$2= $18 Select a blue ball = $3-$2 =$1 Select a white ball =$1-$2 = -$1 Select a black ball =$0-$2= -$2 Hence, Expected value is: = (1/20*18) +(4/20*1) +(8/20*-1) +(7/20* -2) = (18/20) +(4/20) +( -8/20) +( -14/20) = (18+4 -8 -14)/20 = (22 -22)/20 =0/20 = 0

We got an expected value of 0, meaning that the game is a fair game. Here we got expected value exactly 0 means neither profit nor loss if we are looking forward for the profit we should get an expected value more than 0. If we get an expected value 0.05, this means we have a profit of 0.05 on each try.

QUESTION= What is the THEORETICAL RESULTS and how does your experimental probability distribution results compare to them. Were they close? If they weren't close, what are some possible reasons why?

complete the code to determine the highest score value in python

import random

#variables and constants

MAX_ROLLS = 5
MAX_DICE_VAL = 6

#declare a list of roll types

ROLL_TYPES = [ "Junk" , "Pair" , "3 of a kind" , "4 of a kind" ]

pScore = 0
cScore = 0

num_Score = int( input ("Enter a number of round: ") )
print ("\n")
count = 0
while count < num_Score:
#set this to the value MAX_ROLLS

pdice = [0,0,0,0,0]
cdice = [0,0,0,0,0]

#set this to the value MAX_DICE_VAL

pdice = [0,0,0,0,0,0]
cdice = [0,0,0,0,0,0]

#INPUT - get the dice rolls
i = 0
while i < MAX_ROLLS:
pdice[i] = random.randint(1, MAX_DICE_VAL)
cdice[i] = random.randint(1, MAX_DICE_VAL)
i += 1
#end while

#print the player's and computer dice rolls

i = 0
print ( "Player rolled: ", end=" " )
while i < MAX_ROLLS:
print( pdice[i], end = " " )
i += 1
#end while
print ("\n")

i = 0
print ("Computer rolled: ", end=" " )
while i < MAX_ROLLS:
print( cdice[i], end = " " )
i += 1
#end while
  
#load the tally list so we can determine pair, 3 of a kind, etc
i = 0
ptally = [0,0,0,0,0,0]
ctally = [0,0,0,0,0,0]
while i < MAX_ROLLS:
ptally[ pdice[i] - 1 ] += 1
ctally[ cdice[i] - 1 ] += 1
i += 1
#end while

# find out pair, 3 of kind, etc
pmax = ptally[0] # init to first element in tally array
cmax = ctally[0]

i = 1
while i < MAX_DICE_VAL:
if pmax < ptally[i]:
pmax = ptally[i]
#end if

if cmax < ctally[i]:
cmax = ctally[i]
#end if

i += 1
#end while
  
#output - display what was rolled and who won
print("\n")
print(" player rolled: " + ROLL_TYPES[ pmax - 1], end="\n")
print(" computer rolled: " + ROLL_TYPES[ cmax - 1] )

# determine the winner
if pmax > cmax:
print(" player wins!", end="\n" )
print("\n")
pScore += 1
elif cmax > pmax:
print(" computer wins!", end="\n" )
print("\n")
cScore += 1
else:
print(" Tie!", end="\n")
print("\n")

  
count += 1
#end while

The mean cost of domestic airfares in the United States rose to an all-time high of $400 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $115. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $560 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $245 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $310 and $500 (to 4 decimals)?

d. What is the cost for the 5% highest domestic airfares? (rounded to nearest dollar)
$ or - Select your answer -morelessItem 5

The mean cost of domestic airfares in the United States rose to an all-time high of $400 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $105. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $530 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $240 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $300 and $500 (to 4 decimals)?

d. What is the cost for the 5% highest domestic airfares? (rounded to nearest dollar)
$ or - Select your answer -morelessItem 5

The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $120. Use Table 1 in Appendix B. a. What is the probability that a domestic airfare is $555 or more (to 4 decimals)? ( ) b. What is the probability that a domestic airfare is $255 or less (to 4 decimals)? ( ) c. What if the probability that a domestic airfare is between $310 and $470 (to 4 decimals)? ( ) d. What is the cost of the 5% highest domestic airfares? (rounded to the nearest dollar) $ ( ) or -select your answer- more, less.