Please provide solutions to the following problems. Please use Excel to solve the problems and submit the Excel spreadsheet.

A fair coin is tossed 15 times, calculate the probability of getting 0 heads or 15 heads A biased coin with probability of head being .6 is tossed 12 times. What is the probability that number of head would more than 4 but less than or equal to 10. You have a biased dice (with six faces numbered 1,2,3,4,5 and 6) in that odd numbers are thrice as likely as even numbers to show. You toss the dice 10 times. What is the probability that an even number would show up 5 times. If z has a standard normal distribution, calculate the following probability. P(-.3≤z≤10) If x has a normal distribution with mean 15 and standard deviation 2, calculate the following probabilities: P(1≤x<15)

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter

μ = 8t.

(Round your answers to three decimal places.)

(a)

What is the probability that exactly 6 small aircraft arrive during a 1-hour period?

What is the probability that at least 6 small aircraft arrive during a 1-hour period?

What is the probability that at least 11 small aircraft arrive during a 1-hour period?

(b)

What is the expected value and standard deviation of the number of small aircraft that arrive during a 90-min period?

expected value    standard deviation    

(c)

What is the probability that at least 23 small aircraft arrive during a 2.5-hour period?

What is the probability that at most 15 small aircraft arrive during a 2.5-hour period?

A used car salesperson claims that the probability of he selling a used car to an individual looking to purchase a used car is 70% and this probability does not vary from individual to individual. Suppose 5 individuals come to speak to this salesperson one day. If his belief is correct,

1. The probability (to 4 decimal places) that he will sell a car to the first individual he speaks to is ______

2. The probability (to 4 decimal places) that he will not sell a car to any of these 5 individuals is ______

3. The probability (to 4 decimal places) that he will sell a car to exactly 2 individuals is _______

4. The expected number (to 2 decimal places) of individuals he will sell a car to is ­­________

5. The standard deviation (to 4 decimal places) in the number of individuals to whom he will sell a car is

________

6. If the salesperson pays the dealership who allows him to sell cars $1000 per day for the privilege of working at the dealership, and, if he earns $2000 for each car he sells, the expected income per day is

________

A store has N clients per day, where the probability that N will be three is 0.1, that N will be two is 0.4, that N will be one is 0.3. The store never gets more than three clients per day.

(a) Is N binomial? Poisson?

(b) Write the cumulative distribution function for N.

(c) What is the average number of clients per day?

(d) You want to study how many bags of milk each client buys. Half of them buy two bags, a quarter buy 1 bag, and the rest buy none. Let X be the number of bags of milk purchased on a given day. Are X and N independent?

(e) What is the probability that 5 bags will be purchased?

(f) What is the probability that there will be 3 clients and that 5 bags will be purchased?

(g) What is the probability the 5 bags will be purchased given that there are three clients?

(h) Find the probability function of X.

So this is my assignment. My question is, what makes an object a good insulator? Does having a high specific heat alone make a good insulator? Water has a very high specific heat, would it make a good insulator for the material?

Please list off a bunch of common household items with why they are good insulators!

Objective: Construct an insulated device that is designed to retain heat. Heated water will be put into a beaker and the beaker will be put into the device and allowed to cool for 45 minutes.

Construction:

The device must fit within a 15.0 cm × 15.0 cm × 15.0 cm cube.

Devices may be constructed of and contain any materials except for the following prohibited materials: any type of foam, bubble wrap, commercial insulation, metal other than aluminum foil.

Within the device, you must be able to insert and remove a 250 mL standard, unaltered, empty Pyrex beaker.

The device must also easily accommodate the insertion of a thermometer probe all the way through to the bottom of the beaker via a hole at least 1.5 cm in diameter.

Devices may not contain any energy sources (e.g., no electrical components, small battery powered heaters, chemical reactions, etc.) to help keep the water warm.

All parts of the device must not be significantly different from room temperature.

Highest temperature after 45 minutes wins!

For the binomial distribution with n = 10 and p = 0.4, where p is probability of success. Let X be the number of successes.

(a) Find the probability of three or more successes.

(b) Find the µ, E(X), and σ 2 , V ar(X)

A random number generator produces a sequence of 18 digits (0, 1, ..., 9). What is the probability that the sequence contains at least one 3? (Hint: Consider the probability that it contains no 3's. Round your answer to four decimal places.)

Create a case study "Curbing tobacco use in Poland" with the info below.

Health Condition: Tobacco is the second deadliest threat to adult health in the world and causes 1 in every 10 adult deaths. It is estimated that 500 million people alive today will die prematurely because of tobacco consumption. More than three quarters of the world's 1.2 billion smokers live in low- and middle-income countries, where smoking is on the rise. By 2030, it is estimated that smoking-related deaths will have doubled, accounting for the deaths of 6 in 10 people. In the 1980s, Poland had the highest rate of smoking in the world. Nearly three-quarters of Polish men aged 20 to 60 smoked every day. In 1990, the probability that a 15-year-old boy born in Poland would reach his 60th birth­day was lower than in most countries, and middle-aged Polish men had one of the highest rates of lung cancer in the world.

Intervention or Program: In 1995, the Polish parliament passed groundbreaking tobacco-control legislation, which included:

the requirement of the largest health warnings on cigarette packs in the world;

a ban on smoking in health centers and enclosed workspaces;

a ban on electronic media advertisement; and

a ban on tobacco sales to minors.

Health education campaigns and the "Great Polish Smoke-Out" have also raised awareness about the dangers of smoking and have encouraged Poles to quit.

Impact: Cigarette consumption dropped 10 percent between 1990 and 1998, and the number of smokers declined from 14 million in the 1980s to under 10 million at the end of the 1990s. The reduction in smoking led to:

10,000 fewer deaths each year;

a 30 percent decline in lung cancer among men aged 20 to 44;

a nearly 7 percent decline in cardiovascular disease; and

a reduction in low birth weight.

The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution μ = 0.5 and σ = 0.289.

(a) Let x be the sample mean waiting time for a random sample of 19 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.)

(b) Answer Part (a) for a random sample of 50 individuals. (Round your answers to three decimal places.)