Essential Mathematics And Statistics For Science 2nd Edition Graham Currell, Dr. Antony Dowman - Solutions

6.47 Consider a normally distributed population with a population mean of m = 55 and a variance of s2 = 20.a. What is the probability that the sample variance is greater than 40 when n = 16?b. What is the probability that the sample variance is greater than 65 when n = 10?c. What is the probability
6.29 Suppose that we have a population with proportion P = 0.30, and a random sample of size n = 900 drawn from the population.a. What is the probability that the sample proportion is more than 0.32?b. What is the probability that the sample proportion is less than 0.29?c. What is the probability
6.22 In taking a sample of n observations from a population of N members, the variance of the sampling distribution of the sample means is as follows:sx 2 =s2x n# N - n N - 1
6.9 When a production process is operating correctly, the number of units produced per hour has a normal distribution with a mean of 105 and a standard deviation of 20. A random sample of 25 different hours was taken.a. Find the mean of the sampling distribution of the sample means.b. Find the
6.8 Given a population with mean m = 400 and variance s2 = 1, 600, the central limit theorem applies when the sample size is n Ú 25. A random sample of size n = 35 is obtained.a. What are the mean and variance of the sampling distribution for the sample means?b. What is the probability that x 7
6.3 A population contains two million 0s and nine million 1s. What is the approximate sampling distribution of the sample mean in each of the following cases?a. The sample size is n = 4b. The sample size is n = 50 Note: There is a hard way and an easy way to answer this question. We recommend the
6.2 Suppose you are given a die and are asked to roll the die two times and write down the numerical value that results from each roll. You are also told that you can keep rolling as long as you get a different number from what your got on your first roll. Without actually rolling the die, write
6.4 Sampling Distributions of Sample Variances
6.3 Sampling Distributions of Sample Proportions
6.2 Sampling Distributions of Sample Means Central Limit Theorem Monte Carlo Simulations: Central Limit Theorem Acceptance Intervals
6.1 Sampling from a Population Development of a Sampling Distribution
5.99 PowerChina, a Chinese construction company, is building a large, new retail center at the Chengdu Industrial Development Zone, Sichuan. Yao Minhao, one of the project managers, requests that a pile of sand weighing between 140,000 and 142,000 pounds be placed on the newly constructed driveway.
5.88 Suppose data show that a country that has yearly expenses for research and development (R&D) follows a normal distribution with an average of $10 billion. It also indicates that 15% of the countries spend more than $20 billion on R&D per year. Find the percentage of the countries that spend
5.84 An ice-cream truck has an average daily profit of £250 with a standard deviation of £40.a. If a random business day is selected, what is the probability that the day’s profit is more than £280?b. If a random business day is selected, what is the probability that the day’s profit is
5.83 Let X1 and X2 be a pair of random variables. Show that the covariance between the random variables Y1 = 12X1 + X22 and Y2 = 12X1 - X22 is 3 if X1 and X2 have the same variance.
5.82 A manufacturing team leader is evaluating the goods’production forecast times by comparing the actual times with the predicted times, where:actual time = predicted time + forecast error If the predicted time and forecast error are independent of each other, show that the variance of
5.81 A cobbler repairs shoes with normal damages for €2 each. The repaired shoes have a distribution with a mean of 60 and a standard deviation of 10.a. Find the mean daily total revenue earned from the shoes repaired.b. Find the standard deviation of total revenues from the shoes repaired.c.
5.80 An investment plan allows investors to deposit a minimum of £1,000 at the beginning of the term, which pays a fixed return rate of 5% per annum. After a year, investors have to deposit a minimum of£800 with an expected return rate of 3% per annum for the second year and a standard deviation
5.79 The random variable X has probability density function as follows:f1x2 = •x for 0 6 x 6 1 2 - x for 1 6 x 6 2 0 for all other values of xa. Graph the probability density function for X.b. Show that the density has the properties of a proper probability density function.c. Find the
5.78 The ages of a group of executives attending a convention are uniformly distributed between 35 and 65 years. If the random variable X denotes ages in years, the probability density function is as follows:f1x2 = e 1>30 for 35 6 x 6 65 0 for all other values of xa. Graph the probability density
5.77 A consultant knows that it will cost him $10,000 to fulfill a particular contract. The contract is to be put out for bids, and he believes that the lowest bid, excluding his own, can be represented by a distribution that is uniform between $8,000 and $20,000. Therefore, if the random variable
5.75 You have been asked to determine the probability that the contribution margin for a particular product line exceeds the fixed cost of $1420. The total number of units sold is a normally distributed random variable with a mean of 400 and a variance of 900, X|N(400, 900). The selling price per
5.69 A consultant has three sources of income—from teaching short courses, from selling computer software, and from advising on projects. His expected annual incomes from these sources are $40,000,$25,000, and $18,000, and the respective standard deviations are $2,000, $5,000, and $4,000.
5.65 A random variable X is normally distributed with a mean of 14.2 and a variance of 2.25, and a random variable Y is normally distributed with a mean of 13.5 and a variance of 0.81. The random variables have a correlation coefficient equal to 0.74. Find the mean and variance of the random
5.64 A random variable X is normally distributed with a mean of 250 and a variance of 16.81, and a random variable Y is normally distributed with a mean of 360 and a variance of 13.69. The random variables have a correlation coefficient equal to 0.05. Find the mean and variance of the random
5.63 A random variable X is normally distributed with a mean of 50 and a variance of 5.76, and a random variable Y is normally distributed with a mean of 20 and a variance of 9.61. The random variables have a correlation coefficient equal to 0.88. Find the mean and variance of the random variable:W
5.62 A random variable X is normally distributed with a mean of 28 and a variance of 1.44, and a random variable Y is normally distributed with a mean of 13 and a variance of 0.36. The random variables have a correlation coefficient equal to -0.2. Find the mean and variance of the random variable:W
5.61 A random variable X is normally distributed with a mean of 10 and a variance of 4, and a random variable Y is normally distributed with a mean of 15 and a variance of 25. The random variables have a correlation coefficient equal to 0.65. Find the mean and variance of the random variable:W = 2X
5.60 Delivery trucks arrive independently at the Floorstore Regional distribution center with various consumer items from the company’s suppliers. The mean number of trucks arriving per hour is 20. Given that a truck has just arrived answer the following:a. What is the probability that the next
5.54 Given an arrival process with l = 3.0, what is the probability that an arrival occurs in the first t = 2 time units?Application Exercises
5.53 Given an arrival process with l = 5.0, what is the probability that an arrival occurs after t = 5 time units?
5.52 Given an arrival process with l = 5.0, what is the probability that an arrival occurs after t = 7 time units?
5.51 Given an arrival process with l = 0.6, what is the probability that an arrival occurs in the first t = 8 time units?
5.50 Given an arrival process with l = 1.0, what is the probability that an arrival occurs in the first t = 2 time units?
5.49 Bags of a chemical produced by a company have impurity weights that can be represented by a normal distribution with a mean of 12.2 grams and a standard deviation of 2.8 grams. A random sample of 400 of these bags is taken. What is the probability that at least 100 of them contain fewer than
5.43 Given a random sample size of n = 400 from a binomial probability distribution with P = 0.20 do the following:a. Find the probability that the percentage of successes is greater than 0.25.b. Find the probability that the percentage of successes is less than 0.15.c. Find the probability that
5.33 Volvo Cars, a Swedish luxury vehicles company, purchases computer process chips from two suppliers, and the company is concerned about the percentage of defective chips. A review of the records for each supplier indicates that the percentage defectives in consignments of chips follow normal
5.32 Luca Alberti, a Hungarian florist, is considering two alternative investments. In both cases she is unsure about the percentage return but believes that her uncertainty can be represented by normal distributions with the means and standard deviations shown in the accompanying table. Luca wants
5.21 Let the random variable X follow a normal distribution with m = 0.2 and s2 = 0.0025.a. Find the probability that X is greater than 0.4.b. Find the probability that X is greater than 0.15 and less than 0.28.c. Find the probability that X is less than 0.10.d. The probability is 0.2 that X is
5.17 Let the random variable Z follow a standard normal distribution.a. Find P1Z 6 1.162.b. Find P1Z 7 1.732.c. Find P1Z 7 -2.292.d. Find P1Z 7 -1.352.e. Find P11.16 6 Z 6 1.732.f. Find P1 -2.29 6 Z 6 1.162.g. Find P1 -2.29 6 Z 6 -1.352.
5.12 The profit for a production process is equal to $6,000 minus three times the number of units produced. The mean and variance for the number of units produced are 1,000 and 900, respectively. Find the mean and variance of the profit.Application Exercises
5.7 The incomes of all families in a particular suburb can be represented by a continuous random variable. It is known that the median income for all families in this suburb is £55,000 and that 40% of all families in the suburb have incomes above £66,000.a. For a randomly chosen family, what is
5.6 The jurisdiction of a rescue team includes emergencies occurring on a stretch of river that is 4 miles long. Experience has shown that the distance along this stretch, measured in miles from its northernmost point, at which an emergency occurs can be represented by a uniformly distributed
5.5 An analyst has available two forecasts, F1 and F2, of earnings per share of a corporation next year. He intends to form a compromise forecast as a weighted average of the two individual forecasts. In forming the compromise forecast, weight X will be given to the first forecast and weight 11 -
5.4 Using the uniform probability density function shown in Figure 5.7, find the probability that the random variable X is greater than 1.3.Application Exercises
5.6 Jointly Distributed Continuous Random Variables Linear Combinations of Random Variables Financial Investment Portfolios Cautions Concerning Finance Models
5.5 The Exponential Distribution
5.4 Normal Distribution Approximation for Binomial Distribution Proportion Random Variable
5.3 The Normal Distribution Normal Probability Plots
5.2 Expectations for Continuous Random Variables
5.1 Continuous Random Variables The Uniform Distribution
4.104 A fresh fruit juice manufacturer finds a new ingredient that allows the juice to stay fresh for a longer duration than before. The old ingredient shows that 10% of the total quantity of juice produced will stay fresh for less than a month. The expectation is that the new ingredient will
4.103 A fast-food restaurant located at a commercial area indicates that, on average, it receives 20 orders each morning from 7:00 a.m. to 8:00 a.m. Since this is a rush hour, the restaurant has to prepare food items within 10 minutes of receiving an order. Typically, each order is prepared by a
4.102 When buying property, one of the main considerations for a homebuyer is the reputation of a property developer, that is, if they follow good construction practices, offer financial security, and deliver on time. For the previous month, a random sample of the daily number of units sold at a
4.101 Consider a country that imports coal and exports furniture. The value per unit of furniture exported is measured in units of thousands of euros per furniture by the random variable X. The value per unit of coal imported is measured in units of thousands of euros per ton of coal by the random
4.100 George Allen has asked you to analyze his stock portfolio, which contains 10 shares of stock D and 5 shares of stock C. The joint probability distribution of the stock prices is shown in Table 4.10. Compute the mean and variance for the total value of his stock portfolio.Table 4.10 Joint
4.99 A movie theater has 2 halls playing the latest movie 4 times per weekend on average based on Poisson distribution.Assume that the number of times a movie is played at these 2 halls is independent of the other.What is the probability that at least 1 hall plays the movie at least once in any
4.97 On average, a receptionist at a local firm receives 3 packages per hour between 10:00 a.m. and 12:00 p.m.Assume that the distribution of receiving packages is Poisson.a. What is the probability that there are no packages received between 10:00 a.m. and 12:00 noon?b. What is the probability
4.94 John and Steve are participating in an online game.The player who wins three rounds first is declared as the overall winner. Suppose that John is a better player with a probability of 0.7 for winning a game. Assume that the result of the game is independent from each of the game.a. What is the
4.93 Past booking records of a hotel show that 5% of its customers’ online booking will be canceled for a specific reason.a. For a random sample of 10 online bookings, what is the probability that exactly 3 will be canceled?b. For a random sample of 10 online bookings, what is the probability
4.92 A food truck owner, Ayesha, sells each roll for €2.50.She finds that 70% of her customers prefer chicken rolls.Suppose she makes a random selection of 8 customers.State at the outset what assumption she has made.a. Find the probability that at least 2 customers prefer chicken rolls.b. Find
4.91 Suppose the students at the University of Amsterdam, the Netherlands, are classified according their school grades (X), and the number of daily hours spent watching shows on Netflix (Y = 0 for no hours, 1 for one hour, 2 for more than one hour). The joint probabilities in the accompanying
4.89 Develop realistic examples of pairs of random variables for which you would expect to find the following:a. Positive correlationb. Negative correlationc. Zero correlation
4.87 A car salesperson estimates the following probabilities for the number of cars that she will sell in the next week:Number of cars 0 1 2 3 4 5 Probability 0.10 0.20 0.35 0.16 0.12 0.07a. Find the expected number of cars that will be sold in the week.b. Find the standard deviation of the number
4.86 A contractor estimates the probabilities for the number of days required to complete a certain type of construction project as follows:Time (days) 1 2 3 4 5 Probability 0.05 0.20 0.35 0.30 0.10a. What is the probability that a randomly chosen project will take less than 3 days to complete?b.
4.85 As an insurance agent, you advise your client to first consider purchasing a health insurance plan rather than a home insurance plan. How would you respond to the following questions posed by your client?a. Does the advice imply that after purchasing health insurance it is not necessary to get
4.84 A company has 5 representatives covering large territories and 10 representatives covering smaller territories.The probability distributions for the numbers of orders received by each of these types of representatives in a day are shown in the accompanying table.Assuming that the number of
4.82 A restaurant manager receives occasional complaints about the quality of both the food and the service. The marginal probability distributions for the number of weekly complaints in each category are shown in the accompanying table. If complaints about food and service are independent of each
4.81 A college bookseller makes calls at the offices of professors and forms the impression that professors are more likely to be away from their offices on Friday than any other working day. A review of the records of calls, 1/5 of which are on Fridays, indicates that for 16%of Friday calls, the
4.80 A market researcher wants to determine whether a new model of a personal computer that had been advertised on a late-night talk show had achieved more brand-name recognition among people who watched the show regularly than among people who did not.After conducting a survey, it was found that
4.79 The accompanying table shows, for credit-card holders with one to three cards, the joint probabilities for number of cards owned (X) and number of credit purchases made in a week (Y).Number of Cards (X)Number of Purchases in a Week (Y)0 1 2 3 4 1 0.06 0.13 0.09 0.07 0.03 2 0.02 0.07 0.09 0.09
4.78 A real estate agent is interested in the relationship between the number of lines in a newspaper advertisement for an apartment and the volume of inquiries from potential renters. Let volume of inquiries be denoted by the random variable X, with the value 0 for little interest, 1 for moderate
4.77 A researcher suspected that the number of betweenmeal snacks eaten by students in a day during final examinations might depend on the number of tests a student had to take on that day. The accompanying table shows joint probabilities, estimated from a survey.Number of Snacks (Y)Number of Tests
4.76 Consider the following probability distribution:X 1 5 Y 1 0.32 0.15 3 0.24 0.29a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for the linear function W = 5X - 3Y.Application Exercises
4.75 Consider the following probability distribution:X 1 2 Y 2 0.55 0.05 3 0.25 0.15a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for the linear function W = 3X - 2Y.
4.74 Consider the joint probability distribution:X 1 2 Y 0 0.80 0.00 1 0.00 0.20a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for the linear function W = 4X + 3Y.
4.73 Consider the following probability distribution:X 1 2 Y 0 0.1 0.2 1 0.4 0.3a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for the linear function W = X + 3Y.
4.72 Consider the joint probability distribution:X 1 2 Y 0 0.15 0.35 1 0.30 0.20a. Compute the marginal probability distributions for X and Y.b. Compute the covariance and correlation for X and Y.c. Compute the mean and variance for the linear function W = X + Y.
4.66 Compute the probability of 5 successes in a random sample of size n = 12 obtained from a population of size N = 111 that contains 60 successes.
4.65 Compute the probability of 4 successes in a random sample of size n = 6 obtained from a population of size N = 30 that contains 20 successes.
4.64 Compute the probability of 9 successes in a random sample of size n = 25 obtained from a population of size N = 90 that contains 32 successes.
4.63 Compute the probability of 10 successes in a random sample of size n = 16 obtained from a population of size N = 70 that contains 24 successes.
4.53 Determine the probability of fewer than or equal to five successes for a random variable with a Poisson distribution with parameter l = 9.0.Application Exercises
4.52 Determine the probability of fewer than five successes for a random variable with a Poisson distribution with parameter l = 9.0.
4.49 A company receives large shipments of parts from two sources. Seventy percent of the shipments come from a supplier whose shipments typically contain 10%defectives, while the remainder are from a supplier whose shipments typically contain 20% defectives. A manager receives a shipment but does
4.45 We have seen that for a binomial distribution with n trials, each with probability of success P, the mean is as follows:mX = E3X4 = nP Verify this result for the random variable “number of heads” in an experiment tossing three coins by calculating the mean directly from mX = axP1x2 showing
4.41 A small commuter airline flies planes that can seat up to 8 passengers. The airline has determined that the probability that a ticketed passenger will not show up for a flight is 0.2. For each flight the airline sells tickets to the first 10 people placing orders. The probability distribution
4.34 For a binomial probability distribution with P = 0.7 and n = 18, find the probability that the number of successes is equal to 12 and the probability that the number of successes is fewer than 6.Application Exercises
4.33 For a binomial distribution probability with P = 0.87 and n = 23, find the probability that:a. The number of successes is equal to 11.b. The number of successes is fewer than 15.
4.32 For a binomial distribution probability with P = 0.42 and n = 18, find the probability that:a. The number of successes is equal to 7.b. The number of successes is fewer than 10.
4.30 For a Bernoulli random variable with probability of success P = 0.8, compute the mean and variance.
4.28 A factory manager is considering whether to replace a temperamental machine. A review of past records indicates the following probability distribution for the number of breakdowns of this machine in a week.Number of breakdowns 0 1 2 3 4 Probability 0.10 0.26 0.42 0.16 0.06a. Find the mean and
4.27 A store owner stocks an out-of-town newspaper that is sometimes requested by a small number of customers.Each copy of this newspaper costs her 70 cents, and she sells them for 90 cents each. Any copies left over at the end of the day have no value and are destroyed.Any requests for copies that
4.26 The manager at a firm in Tokyo wants to organize a trip for his team in the summer of 2020, but some employees have already applied for leave. To be better prepared, he estimates the probabilities of the employees who are taking day(s) off during the summer season in the following table.Number
4.25 One of the leading retail banks in China is the Postal Savings Bank of China, located in Beijing. Suppose the number of arrivals per minute at the bank, which has around 40,000 outlets, was recorded over a period of 200 minutes with the results shown in the table below.Arrivals 0 1 2 3 4 5 6 7
4.21 A municipal bus company has started operations in a new subdivision. Records were kept on the numbers of riders on one bus route during the early-morning weekday service. The accompanying table shows proportions over all weekdays.Number of riders 20 21 22 23 24 25 26 27 Proportion 0.02 0.12
4.20 Forest Green Brown, Inc., produces bags of cypress mulch. The weight in pounds per bag varies, as indicated in the accompanying table.Weight in pounds 44 45 46 47 48 49 50 Proportion of bags 0.04 0.13 0.21 0.29 0.20 0.10 0.03a. Graph the probability distribution.b. Calculate and graph the
4.19 A company specializes in installing and servicing central-heating furnaces. In the prewinter period, service calls may result in an order for a new furnace. The following table shows estimated probabilities for the numbers of new furnace orders generated in this way in the last two weeks of
4.18 An automobile dealer calculates the proportion of new cars sold that have been returned a various numbers of times for the correction of defects during the warranty period. The results are shown in the following table.Number of returns 0 1 2 3 4 Proportion 0.28 0.36 0.23 0.09 0.04a. Graph the
4.17 Consider the probability distribution function.X 0 1 Probability 0.40 0.60a. Graph the probability distribution function.b. Calculate the cumulative probability distribution function.c. Find the mean of the random variable X.d. Find the variance of X.

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Essential Mathematics And Statistics For Science 2nd Edition Graham Currell, Dr. Antony Dowman - Solutions

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