The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of inde
A random variable Y is uniformly distributed over a range of 0 to 2*pi. Another random variable X is related to Y by X=cos(Y). Find the probability density function of X.
1. A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully. 2. The probability is 1 in 4,000,00
Problem 1. A local bank reports that 80 percent of its customers maintain a checking account, 60 percent have a savings account, and 50 percent have both. If a customer is chosen at random, what is the probability the customer has either a checking or a savings account? What is the probability the customer
Problem 2. A recent study of the hourly wages of maintenance crew members for major airlines showed that the mean hourly salary was $20.50, with a standard deviation of $3.50. If we select a crew member at random, what is the probability the crew member earns: a. Between $20.50 and $24.00 per hour? b. More than $24.00 per hour?
1. During summer weekdays, boats arrive at the inlet drawbridge according to the Poisson distribution at a rate of 3 per hour. In a 2 hour period, what is the probability that 2 boats arrive? Please provide the answer in the form 0.xxxx or .xxxx. 2. A researcher wants to simulate sunny and rainy days in her town for a 3
I have been working with M&M's throughout this classes course. From the data I gathered I developed histograms and calculated descriptive statistics. Based on this data I then can make judgments on what I can expect to see when I buy packages of M&M's at the store. To do this I calculate what is called confidence limits
According to a survey conducted by Peter, 37% of adults are concerned that employers are monitoring phone calls Use the binomial distribution formula to calculate the probability that a) out of 5 adults, none is concerned. b) out of 5 adults all are concerned. c) out of 5 adults, exactly 3 are concerned that employers are m
A Tamiami shearing machine is producing 10 percent defective pieces, which is abnormally high. The quality control engineer has been checking the output by almost continuous sampling since the abnormal condition began. What is the probability that in a sample of 10 pieces: a. Exactly 5 will be defective? b. 5 or more will
Risk neutral probability and value of call option: 17. A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 10% or fall by 10%. Consider a six-month European call option with a strike price of $105. The risk-free rate is 8%. What is the risk-neutral probability of a 10% rise in both quarters? a. 0.10 b. 0.24 c. 0.36 d. 0.60 e. 0.84 18. A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 10% or fall by 10%. Consider a six-month European call option with a strike price of $105. The risk-free rate is 8%. What is the value of the call option? a. $6.25 b. $5.55 c. $5.00 d. $4.50 e. $4.05
17. A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 10% or fall by 10%. Consider a six-month European call option with a strike price of $105. The risk-free rate is 8%. What is the risk-neutral probability of a 10% rise in both quarters? a. 0.10 b. 0.24 c. 0.3
X=age(years) 60 61 62 63 64 p(death at this age 0.00756 0.00825 0.00896 0.00965 0.01035 a) What is the probability that sara will die in her 60th year? using this probability and the $50,000 death benefits, what is the expected loss? b) Repeat part(a) for years 61,62
2 cards drawn from a 52 but before the second card is drawn you put the first one back and reshuffle the deck a) Are the outcomes on the two cards independent and why? b) Find p(3 on first card and 10 on second), find p(10 on the first card and 3 on second). c) Find the probability of drawing a 10 and an 3 in either order.
Height of arch, feet:.....3-9......10-29.....30-49....50-74.....75+ # of arches in park:......111........96..........30.........33........18 Use the information to estimate the probability that the height of the arch opening is a)3 to 9 feet b)30 feet or taller c)10-74 feet
Estimate a probability that a seed from new plant will germinate a random sample of 3000 seeds, of those seeds 2430 germinated a) Use relative frequencies to estimate that the seed will germinate, estimate the probability that the seed will not germinate b) What is the sample space for this problem and does it add up tp 1?
The distance between major cracks in highway follows an exponential distribution with a mean of 5 miles. a) What is the probability that there are no major cracks in a 10 mile stretch of highway. b) What is the probability there is 2 major cracks in a 10 mile stretch of highway c) what is the std deviation of the dista
Assume that the life of a roller bearing follows a Weibull Distribution with parameters: Beta = 2 and delta = 10000 hours. a) determine the probability that a bearing lasts at leasts 8000 hrs. b) Determine the mean time until failure of a bearing. c) If 10 bearings are in use and failures occur independently what is the pro
The amount of time a bank teller spends with each customer has a population mean µ = 3.10 minutes ...
The amount of time a bank teller spends with each customer has a population mean µ = 3.10 minutes and a standard deviation σ = 0.60. If a random sample of 36 customers is selected, a. What is the probability that the average time will be at least 3 minutes? b. What is the probability the average time will be between
10. Wildlife Hummingbirds Selasphorus sasin is the scientific name for what is commonly called "Allen Hummingbird" This beautiful hummingbird lives on the west coast of the United States and is named C.A. Allen (1841-1930) , who studied these birds extensively. Let x be a random variable that represents the incubation time for
Please help with the following problems. 3. Use this table to answer questions #3 through #5. Some students were asked if they carry a credit card. Here are the responses. Class______ | Credit Card Carrier | Not a Credit Card Carrier | Total Freshman______________33_______________________27________________60 Sophomore____
During 2001, 61.3% of US households purchased ground coffee.These households spent an average of $36.16 on ground coffee during the year. Consider the annual ground coffee expenditures for households purchasing ground coffee, assuming that these expenditures are approximately distributed as a normal random variable with a mean o
1. On average, 40% of U.S. beer drinkers order light beer. (5 points) a. What is the probability that none of the next eight customers who order beer will order light beer? b. What is the probability that one customer will? c. What is the probability that two customers will? d. What is the probability that fewer than three w
1. Some normal probability distributions may have the same mean, but their standard deviation may be different True or False 2. As the sample size increases, the standard error of the sample mean increases. True or False 3. Which of the following statement(s) about the normal probability distribution is/are true?
Body Types: A study on body types gave the following results: 45% were short; 25% were short and overweight; and 24% were tall and not overweight. Find the probabilities that a person is the following. a. Overweight b. Short, but not overweight c. Tall and overweight
Quality control: Syringes The quality control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of 8 syringes taken from the batch. Suppose the batch contains 1% defective syringes. a.) Make a histogram showing the probabilities of r=0, 1,2,3,4,
Problem 10) You roll two fair dice, one red and one green. a) What is the probability of getting a number less than 5 on both? b) What is the probability of getting a sum of 9 on the two dice? c) What is the probability of getting a 5 on both?
Describe a real-life situation where Pascal's Triangle can be used to calculate probability. Is this the best method for solving your calculation? If yes, why? If not, what other principle would you use?
4. Sociology: Ethics. The one-time fling! Have you ever purchased an article of clothing (dress, sports, jackets, etc.) worn the item once to a party, then returned the purchase? This is called the one time fling. About 10% of all adults deliberately do a one-time fling and feel no guilt about it. (Source: "Are you Normal?" By B
The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of
I need some guidance in how to calculate probabilities without knowing the std deviation. Population = 3005 calculate P(x-bar > 50.8) for sample size of n = 253 calculate P(x-bar > 50.6) for sample size of n = 134 calculate P(x-bar > 51) for sample size of n = 119 Then combine the two probabilities 51 a
1. A financial analyst estimates that the probability that the economy will experience a recession in the next 12 months is 20%. She also believes that if the economy enters a recession, the probability that her mutual fund will increase in value is 20%. If there is no recession the probability that the mutual fund will increase