In a population of interest, we know that, 77% drink coffee, and 23% drink tea. Assume that drinking coffee and tea are disjoint events in this population. We also know coffee drinkers have a 30% chance of smoking. There is a 13% chance of smoking for those who drink tea.

1. Five individuals are randomly chosen from this population. What is the probability that four of them drink coffee?

2. Five individuals are randomly chosen from this population. What is the probability that the first four drink coffee and the last one drinks tea?

3. Five individuals are randomly chosen from this population. What is the expected number (population mean) of coffee drinkers?

4. Five individuals are randomly chosen from this population. Find the standard deviation for the number of coffee drinkers.

5. A person is randomly chosen from this population. What is the probability that the person smokes?

1. A grocery store counts the number of customers who arrive during an hour. The average over a year is 29 customers per hour. Assume the arrival of customers follows a Poisson distribution. (It usually does.) Find the probability that at least one customer arrives in a particular one minute period. Round your answer to 3 decimals. Find the probability that at least two customers arrive in a particular 2 minute period.

2. Label each as one of the following

Exponential

Poisson

Binomial

Uniform

1. a constant probability density and charts as a rectangle
2. fixed number of trials with only 2 possible outcomes and the trials are independent  
3. models the time until some specifi event occurs such as equipment failure  
4. events happen with a known average rate and independently of the time since the last event  

1.Your Username for your company computer is three letters followed by five single digit numbers. The Letters can be repeated but the digits cannot be repeated. Find total possible number of usernames for your company"s computer system.

2.If a pair of fair dice is rolled find following probability that a number other than seven or eleven is rolled such that it is given that one of the two die is a two or a four.?

3.It is estimated that 2% pregnancies are the result of in vitro fertilization. The chance of multiple births from in vitro fertilization is 48%. The chance of multiple births from normal methods is 3%.

a) What is the probability a couple used in vitro fertilization and it resulted in a non-multiple birth?

b) If a multiple birth did not occur, what is the probability that it is the result of normal methods?

An experiment consists of rolling 1 red die, 1 white die, and 1 blue die and noting the result of each roll. The dice are fair, and all out comes are equally likely,

What is the probability that the SUM of the results on the three dice is 7?

What is the probability that the sum is an odd number?

Please explain in detail.  

A random sample of 1000 eligible voters is drawn. Let X = the number who actually voted in the last election. It is known that 60% of all eligible voters did vote. a) Find the approximate probability that 620 people in the sample voted, and b) Find the approximate probability that more than 620 people in the sample voted.

Frank Ocean decides to play roulette. This game is attractive because the house advantage is small. If Frank plays and wins big, which of the following is true?

A certain type of tomato seed germinates 90% of the time. A backyard farmer planted 25 seeds.

a) What is the probability that exactly 20 germinate? Carry answer to the nearest ten-thousandths.

b) What is the probability that 20 or more germinate? Carry answer to the nearest ten-thousandths.

c) What is the probability that 24 or fewer germinate? Carry answer to the nearest ten-thousandths. d) What is the expected number of seeds that germinate? Carry answer to the nearest tenths.

A random sample of 6IC's is taken from a large consignment and tested in two independent

stages. The probability that an IC will pass either stage is p.All the 6IC's are tested at the first stage.

If 5 or more pass the test, those which pass are tested at the second stage.The consignment is accepted if

there is at most one failure at each stage.

a) what is the probability that stage two of the test will be required?

b) the number of items expected to enter stage 2

c) the probability of accepting the consignment

Monica claims that she randomly selected answers to ten multiple choice questions (A-E). She correctly answered seven of them. Let X be the number questions answered correctly out of ten

•If she did randomly guess, what’s the probability that any given answer is correct?

•What’s the probability that she guessed 7 questions correctly, by chance alone?

•What’s the probability that she guessed less than 7 questions correctly, by chance alone?

A particular intersection in a small town is equipped with a surveillance camera. The number of traffic tickets issued to drivers passing through the intersection follows the Poisson distribution and averages 4.5 per month.

a. What is the probability that 5 traffic tickets will be issued at the intersection next​ month?

b. What is the probability that 3 or fewer traffic tickets will be issued at the intersection next​ month?

c. What is the probability that more than 6 traffic tickets will be issued at the intersection next​ month?