QuestionAnswered step-by-step1.Given that x is a normal variable with mean=49and standard…1.Given thatxis a normal variable with mean?=49and standard deviation?=6.2, find the following probabilities. (Round your answers to four decimal places.)(a) P(x=60)(b) P(x=50)(c) P(50=x=60)2.Find z such that 13% of the area under the standard normal curve lies to the right of z. (Round your answer to two decimal places.)3.Find z such that 59% of the standard normal curve lies between -z and z. (Round your answer to two decimal places.)4.Blood type AB is found in only 3% of the population.If275peopleare chosen at random, find the probability of the following. (Use the normal approximation. Round your answers to four decimal places.)(a) 5 or more will have this blood type(b) between 5 and 10 will have this blood type5.The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of8.9minutes and a standard deviation of2.0minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)(a) less than 10 minutes(b) longer than 5 minutes(c) between 8 and 15 minutes6.The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed, with mean?=37minutes and standard deviation?=8minutes. (Round your answers to four decimal places.)(a) What is the probability that a first interview will last 40 minutes or longer?(b)Fourfirst interviews are usually scheduled per day. What is the probability that the average length of time for thefourinterviews will be 40 minutes or longer?7.Supposexhas a distribution with?=25and?=20.(a) If a random sample of sizen=37is drawn, find?x,?xandP(25=x=27). (Round?xto two decimal places and the probability to four decimal places.)?x=?x=P(25=x=27) =(b) If a random sample of sizen=63is drawn, find?x,?xandP(25=x=27). (Round?xto two decimal places and the probability to four decimal places.)?x=?x=P(25=x=27) =(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)The standard deviation of part (b) is —Select— the same as larger than smaller than part (a) because of the —Select— same smaller larger sample size. Therefore, the distribution about?xis —Select— wider the same narrower .8.Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put81tons of coal into each car. The actual weights of coal loaded into each car arenormally distributed, with mean?=81tons and standard deviation?=1.1ton.(a) What is the probability that one car chosen at random will have less than80.5tons of coal? (Round your answer to four decimal places.)(b) What is the probability that40cars chosen at random will have a mean load weightxof less than80.5tons of coal? (Round your answer to four decimal places.)(c) Suppose the weight of coal in one car was less than80.5tons. Would that fact make you suspect that the loader had slipped out of adjustment?Yes or NoSuppose the weight of coal in40cars selected at random had an averagexof less than80.5tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? A. Yes, the probability that this deviation is random is very small. B. Yes, the probability that this deviation is random is very large.C. No, the probability that this deviation is random is very small. D. No, the probability that this deviation is random is very large.9.In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.It is known that85%of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces64new products, find the following probabilities. (Round your answers to four decimal places.)(a) within 2 years 47 or more fail(b) within 2 years 58 or fewer fail(c) within 2 years 15 or more succeed(d) within 2 years fewer than 10 succeed10.In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.What are the chances that a person who is murdered actually knew the murderer? The answer to this question explains why a lot of police detective work begins with relatives and friends of the victim! About63%of people who are murdered actually knew the person who committed the murder.Suppose that a detective file in New Orleans has65current unsolved murders. Find the following probabilities. (Round your answers to four decimal places.)(a) at least 35 of the victims knew their murderers(b) at most 48 of the victims knew their murderers(c) fewer than 30 victims did not know their murderers(d) more than 20 victims did not know their murderers11.Allen’s hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther. Suppose a small group of 20 Allen’s hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen’s hummingbirds have a normal distribution, with ? = 0.26 gram.(a) Find an 80% confidence interval for the average weights of Allen’s hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) A.normal distribution of weights B.uniform distribution of weights C.n is large D.? is unknown E.? is known(c) Interpret your results in the con of this problem. A.We are 20% confident that the true average weight of Allen’s hummingbirds falls within this interval. B.We are 80% confident that the true average weight of Allen’s hummingbirds falls within this interval.C.The probability that this interval contains the true average weight of Allen’s hummingbirds is 0.80. D.The probability that this interval contains the true average weight of Allen’s hummingbirds is 0.20.(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.12 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)=hummingbirds12.Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken five blood tests for uric acid. The mean concentration was x = 5.28 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with ? = 1.87 mg/dl.(a)Find a 95% confidence interval for the population mean concentration of uric acid in this patient’s blood. What is the margin of error? (Round your answers to two decimal places.)lower limit=upper limit=margin of error=(b)What conditions are necessary for your calculations? (Select all that apply.) A.normal distribution of uric acid B.uniform distribution of uric acid C.? is unknown D.? is known E.n is large(c)Interpret your results in the con of this problem.A. We are 95% confident that the true uric acid level for this patient falls within this interval.B. The probability that this interval contains the true average uric acid level for this patient is 0.05.C. We are 5% confident that the true uric acid level for this patient falls within this interval.D. The probability that this interval contains the true average uric acid level for this patient is 0.95.(d)Find the sample size necessary for a 95% confidence level with maximal margin of error E = 1.12 for the mean concentration of uric acid in this patient’s blood. (Round your answer up to the nearest whole number.) blood tests13.Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 45 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.90 ml/kg for the distribution of blood plasma.(a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.)the distribution of volumes is normalA.? is unknownB.? is knownC .n is largeD. the distribution of volumes is uniform(c) Interpret your results in the con of this problem.A.We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.B.The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.C.We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.D.The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.(d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.70 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)male firefighters14.What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that ? is known to be $1.98 per 100 pounds.(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)lower limit $upper limit $margin of error $(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.31 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)farming regions(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)lower limit $upper limit $margin of error $15.Thirty-two small communities in Connecticut (population near 10,000 each) gave an average of x = 139.1 reported cases of larceny per year. Assume that ? is known to be 43.7 cases per year.(a)Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)lower limit=upper limit=margin of error=(b)Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)lower limit=upper limit=margin of error=(c)Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)lower limit=upper limit=margin of error=16.At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Sixty-three wind speed readings gave an average velocity of x = 1075 cm/sec. Based on long-term experience, ? can be assumed to be 260 cm/sec.(a)Find a 95% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number.)lower limit= cm/secupper limit= cm/sec17.Jobs and productivity! How do banks rate? One way to answer this question is to examine annual profits per employee. The following is data about annual profits per employee (in units of 1 thousand dollars per employee) for representative companies in financial services. Assume ? 11.0 thousand dollars.46.7 58.6 57.9 43.2 39.7 34.1 51.6 55.1 42.5 33.0 33.636.9 27.0 47.1 33.8 28.1 28.5 29.1 36.5 36.1 26.9 27.828.8 29.3 31.5 31.7 31.1 38.0 32.0 31.7 32.9 23.1 54.943.8 36.9 31.9 25.5 23.2 29.8 22.3 26.5 26.7 (a) Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.)thousand dollars(b) Let us say that the preceding data are representative of the entire sector of (successful) financial services corporations. Find a 75% confidence interval for ?, the average annual profit per employee for all successful banks. (Round your answers to two decimal places.)lower limit thousand dollarsupper limit thousand dollars(C) Find a 90% confidence interval for ?, the average annual profit per employee for all successful banks. (Round your answers to two decimal places.)lower limit thousand dollarsupper limit thousand dollars18.Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of 1 thousand dollars per employee) for companies in retail sales. Assume ? 4.2 thousand dollars.4.5 6.7 4.1 8.3 7.9 5.1 8.2 5.8 2.6 2.9 8.1 -1.911.9 8.2 6.4 4.7 5.5 4.8 3.0 4.3 -6.0 1.5 2.9 4.8-1.7 9.4 5.5 5.8 4.7 6.2 15.0 4.1 3.7 5.1 4.2 (a) Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.)thousand dollars per employee(b) Let us say that the preceding data are representative of the entire sector of retail sales companies. Find an 80% confidence interval for ?, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)lower limit thousand dollarsupper limit thousand dollars (C) Find an 95% confidence interval for ?, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)lower limit thousand dollarsupper limit thousand dollars19.How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 54 readings (for a balloon in equilibrium) gave a mean temperature of x = 97C. For this balloon, ? 23C.(a) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.)lower limit Cupper limit CMathStatistics and ProbabilityMA 114Share Question

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