The probability that a randomly selected 3​-year-old male garter snake will live to be 4 years old is 0.99244.
​(a) What is the probability that two randomly selected 3​-year-old male garter snakes will live to be 4 years​ old?
​(b) What is the probability that eight randomly selected 3​-year-old male garter snakes will live to be 4 years​ old?
​(c) What is the probability that at least one of eight randomly selected 3​-year-old male garter snakes will not live to be 4 years​ old? Would it be unusual if at least one of eight randomly selected 3​-year-old male garter snakes did not live to be 4 years​ old?

Suppose you toss a fair coin 10 times.

(a) Calculate the probability of getting at least 6 heads, using the exact distribution.

(b) Now repeat the calculate above, but approximate the probability using a normal random variable. Do your calculation both with and without the histogram correction. Which one is closer to the true answer?

Now suppose you toss a fair coin 1000 times.

(c) What is the probability of getting at least 520 heads? You can approximate this using a normal with the appropriate mean and variance. Do this with and without the histogram correction. (Does it matter if you use this correction?)

(d) What is the probability of getting at least 600 heads? Calculate this however you want.

John runs a computer software store. Yesterday he counted 139 people who walked by the store, 62 of whom came into the store. Of the 62, only 22 bought something in the store.

(a) Estimate the probability that a person who walks by the store will enter the store. (Round your answer to two decimal places.)


(b) Estimate the probability that a person who walks into the store will buy something. (Round your answer to two decimal places.)


(c) Estimate the probability that a person who walks by the store will come in and buy something. (Round your answer to two decimal places.)


(d) Estimate the probability that a person who comes into the store will buy nothing. (Round your answer to two decimal places.)

the statement of the problem:

"Buses arrive at a bus station at a rate 2 buses per minute. the arrival of buses occurs at random times according to a Poisson scatter on (0, infinity). Show all your work for each part."

a. what is the probability that no bus arrives between t = 0 and t = 30 seconds?

b. what is the probability that the third bus arrives after t = 3 minutes?

c. what is the probability that the 5-th bus arrives within 1 minute of the 4-th bus?

d. what is the probability that the 1-st bus arrives in less than 1 minute and fewer than 2 buses arrive between t = 3 and t = 5 minutes.

Suppose 88% of all batteries from a supplier have acceptable voltages. A certain type of flashlight requires two type-D batteries, and the flashlight will work only if both its batteries have acceptable voltages. Treat all batteries and flashlights as independent of each other.

(a) In 20 randomly selected batteries, what is the probability that 19 or 20 have acceptable voltages?

(b) Suppose 20 randomly selected batteries are placed into 10 flashlights. What is the probability that at least 9 of the flashlights function properly? Hint: Determine the probability that a single flashlight functions, then use that to find the desired probability.

(c) You probabilities in parts a and b should differ slightly. Why do you think this is?

Data from the Bureau of Labor Statistics’ Consumer Expenditure Survey (CE) show that annual expenditures for cellular phone services per consumer unit increased from $237 in 2001 to $634 in 2007. Let the standard deviation of annual cellular expenditure be $52 in 2001 and $207 in 2007.

John knows that monthly demand for his product follows a normal distribution with a mean of 2,500 units and a standard deviation of 425 units. Given this, please provide the following answers for John.

a. What is the probability that in a given month demand is less than 3,000 units?

b. What is the probability that in a given month demand is greater than 2,200 units?

c. What is the probability that in a given month demand is between 2,200 and 3,000 units?

d. What is the probability that demand will exceed 5,000 units next month?

e. If John wants to make sure that he meets monthly demand with production output at least 95% of the time. What is the minimum he should produce each month?

A small regional carrier accepted 20 reservations for a particular flight with 17 seats. 13 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 40% chance, independently of each other.
Find the probability that overbooking occurs.
Find the probability that the flight has empty seats.

Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use some form of technology to find the probability distribution given the probability p=0.299p=0.299 of success on a single trial.
(Report answers accurate to 4 decimal places.)

Question 6 options:

The length of western rattlesnakes are normally distributed with a mean of 60 inches and a standard deviation of 4 inches.

Enter answers as a decimal rounded to 4 decimal places with a 0 to the left of the decimal point.
Do not enter an answer as a percent.

Suppose a rattlesnake is found on a mountain trail:

a. What is the probability that the rattlesnakes' length will be equal to or less than 54.2 inches?

b. What is the probability its' length will be equal to or greater than 54.2 inches?

c. What is the probability that the rattlesnakes' length will be between 54.2 inches and 65.8 inches?

d. Suppose a nest of 16 rattlesnakes are found on the mountain trail:

What is the probability that the average length of the rattlesnakes will be 60.85 inches or more?

You are offered a European Call option. This means you will have the option, but not the
obligation, to buy the stock at the strike price K of $100.

The price of the stock today is
$90. Your time discount rate is Beta=0.98, the risk-less rate of interest is 3%.

The price of the stock follows the following process over two periods: with probability
75% the price will not change from period 0 to period 1, but with probability 25% will go
up to $130. Then from period 1 to period 2, with probability 25% the price will stay the
same, and with probability 75% the price will go down by 20%.
How much would you be willing to pay as of period 0 for this option

Show work please!