A. Simulate 50 observations from a normal distribution with mean 0 and standard deviation 1. make a normal plot. b. Repeat the simulation of (a) but use an exponential distribution with mean = 1 how does the shape of the plot compare to the plot using normal data? c. Repeat the simulation in (a) but use a uniform distribu
1. The total area under a probability distribution graph is equal to _____. 2. The normal distribution is a _____ distribution. 3. Discuss the shape of the normal curve. 4. Define "confidence level" in estimating mu, the population mean.
See attached file for full problem description. summary of options purchased at beginning of 4th quarter with 3 months to expiration (european style options) position shares premium strike price long calls 63,000 $20.45 $110 long puts 63,000 $13.15 $110 beginning end 4th Quarter 4th Quarter underly
Option Valuation and Strategies: call option, Black-Scholes, Put-call parity, arbitrage opportunity, hedge ratio, delta, hedge the position
1. A call option is the right to buy stock at $50 a share. Currently the option has six months to expiration, the volatility of the stock (standard deviation) is 0.30, and the rate of interest is 10 % a) What is the value of the option according to the Black-Scholes model if the price of the stock is $45, $50, or $55? b) What
An executive at Westinghouse drives from his home in the suburbs near Pittsburgh to his office in the center of the city. The driving times are normally distributed with a mean of 35 minutes and a standard deviation of 8 minutes.
An executive at Westinghouse drives from his home in the suburbs near Pittsburgh to his office in the center of the city. The driving times are normally distributed with a mean of 35 minutes and a standard deviation of 8 minutes. a. In what percent of the days will it take him less than 30 minutes to drive to work? b.
1. The use of simulation to examine corporate operations (industrial dynamics), national economies (econometric models), and urban governments is known as A. Monte Carlo Methods B. Operational Gaming C. System Simulation D. Queuing Methods 2. PERT A. Is a network technique that uses three time estimat
14. Approximately ______ of the area (cases or observations) under the normal curve is found between 1 standard deviation above and 1 standard deviation below the mean. 15. What percentage of area (or cases or observations) is found above a z value of 1.96? ._____ 16. A random sample of 20 observations is drawn from a
The number of passengers on the Carnival Sensation during one-week cruises in the Caribbean follows the normal distribution. The mean number of passengers per cruise is 1,820 and the standard deviation is 120. 1. What percent of the cruises will have between 1,820 and 1,970 passengers? 2. What percent of the cruises will ha
The scores of the GRE exam are transformed so they have a mean of 500 and a standard deviation of 100.
1. The scores of the GRE exam are transformed so they have a mean of 500 and a standard deviation of 100. The scores are known to be normally distributed. What is the percentage of students that score below 750? 2. In 10 Bernoulli trials, 130 outcomes contain exactly three successes. Is this a true statement? 3.The pr
13. The quality assurance department for Pepsi Distributors, Inc. maintains meticulous records on the bottling line for two-liter Pepsi bottles. Records indicate that the process follows the normal probability distribution with a mean amount per bottle of 2.01 liters and a standard deviation of 0.025 liters. The foreman random
#2 There is some concern that exposure to gases used in anesthesiology may be harming the health of anesthesiologists. In one study of 525 Michigan nurse anesthesiologists, 10 reported a new malignancy other than skin cancer during the previous year. 2.1 What is the appropriate choice of distribution for the incidence of ne
Finding Probability and Sample size using Normally Distributed Sample. For complete description of the questions, please see the problems.
Question (1) The price of shares of Bank of Florida at the end of trading each day for the last year followed the normal distribution. Assume there were 240 trading days in the year. The mean price was $42.00 per share and the standard deviation was $2.25 per share. a. What percent of the days was the price over $45.00? How
See the attached file. 16. For a normal population with mean=50 and standard deviation=10, what is the probability of obtaining a sample mean greater than 52 for each of the following sample sizes n=5 _________________% n=10 _________________% n=50 _________________% n=100 _________________% An assessment of optimism
1. Find the area under the Normal Distribution from the mean to a z-score of -2.07. 2. Find the z-score that corresponds to an area of 0.5557 under the Normal Distribution. 3. The average age of statistics students nationwide is 22. The standard deviation is 2.5 years. Assume the age is a normally distributed variable
1. Given that z is a standard normal random variable, compute the following probabilities. a. P(-1≤z≤0) b. P(-1.5≤z≤0) c. P(-2<z<0) d. P(-2.5≤z≤0) e. P(-3≤z≤0) 2. Given that z is a standard normal random variable, compute the following probabilities. a. P(0≤z≤.83) b. P(-1.57≤z≤0) c. P(z>44) d
The following table displays information on the abortion rate- the number of abortions per 1,000 women- for each U.S. state and the District of Columbia in 2000. a. What are the mean and the standard deviation for the abortion rate for all states? b. Using the information from (a), how many states fall more than 1 standard dev
If Chebychev Inequality gives the lower bound for probability. For the present problem the lower bound for the probability is 0.75 and actual probability is 0.87. There is no contradiction between empirical rule and Chebychev Inequality Given percentage (87%), does the empirical rule apply? What does the Empirical Rule s
Give a brief description of the variable and whether the scale of measurement is nominal, ordinal, interval, or ratio, and why. The Measurement Principles Nominal : People or objects with the same scale value are the same on some attribute. The values of the scale have no 'numeric' meaning in the way that you usually think
The mean annual salary for employees at Company X is $78,000. If we assume a standard deviation of $12,000, what is the sampling distribution of the sample mean for samples of size 121?
1. A population of unknown shape has a mean of 75. you select a sample of 40. the standard deviation of the sample is 5. What is the probability that the sample mean is between 76 and 77? a. 0.3980 b. 0.8905 c. 0.0081 d. 0.3943 2. a population has a mean of 50 and a standard deviation of 12. FOr samples of size 9, sam
Normal Distribution: For each letter grade, find the minimum score. What do you think of this grading scheme?
Grades on a midterm exam in a large biochemistry class are normally distributed with a mean of 75 and standard deviation of 9. The instructor wants to assign an A grade to the top 10% of scores, a B grade to the next 10%, and so on, with an F grade to all scores below the 60th percentile. For each letter grade, find the minimu
1 The distribution of purchase amounts of customers of a popular retail store is normal with a mean of $25 and a standard deviation of $8. a. What percentage of customers spends less than $35? b. What percentage of customers spends between $15 and $35? c. Find the dollar amount such that 80% of customers spend at least t
Suppose that IQ scores in one region are normally distributed with a standard deviation of 16. Suppose also that exactly 55% of the individuals from this region have IQ scores of greater than 100 (and that 45% do not). What is the mean IQ score for this region? Carry your intermediate computations to at least four decimal plac
21. A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa? 23. The time to complete a final examinat
3. Delta airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. A. Show the graph of the probability density function for flight time B. What is the probability that the flight
The lifetime of a certain brand of batteries are known to be normally distributed with a mean of 1600 hours and a standard deviation of 400 hours. A random sample of 64 of these batteries is taken. What is the probability that the sample mean lifetime is more than 1500 hours?
A random sample of size 25 is taken from a normal population having a mean of 80 and a standard deviation of 5. A second random sample of size 36 is taken from a different normal population having a mean of 75 and a standard deviation of 3. Find the probability that the sample mean computed from the 25 measurements will exceed
SAT scores have a mean 500 and a standard deviation of 100 ACT scores have a mean of 18 and a standard deviation of 6. a. If a school accepts the top 10% what is the minimum ACT score and the minimum SAT score. b. If a school accepts the top 20% what is the minimum ACT and SAT score. c.If a school accepts the top 60% wh
Please show all work such as formula commands. The amount of money that a family of four will spend at Kings Island, including the food and souvenirs, is $130 with a standard deviation of $12. Assume that this distribution is normal. 1. Find the probability that a particular family of four selected at random spends between
Finding probability using Normal Distribution Question : Ina normal distribution, find the probability that a term picked at random has a z score: (a) Above z=1.85 (b) Below z= -1.23 (c) Between z= 1.5 and z= .5