Homework answers / question archive / Problem 1 In a survey of 920 people aged from 18 through 84 years, of whom 80 belonged to the Millenial Generation (18 – 36), 220 belonged to Generation X (37 – 52), 200 belonged to the Baby Boom Generation and the rest belonged to the Silent generation (71+), the following question was asked: Who has slept with a cell phone nearby? 85%, 70%, 50%, and 20% of the people from the Millenial Generation, Generation X, the Baby Boom Generation, and the Silent generation, respectively, answered in the affirmative

Problem 1 In a survey of 920 people aged from 18 through 84 years, of whom 80 belonged to the Millenial Generation (18 – 36), 220 belonged to Generation X (37 – 52), 200 belonged to the Baby Boom Generation and the rest belonged to the Silent generation (71+), the following question was asked: Who has slept with a cell phone nearby? 85%, 70%, 50%, and 20% of the people from the Millenial Generation, Generation X, the Baby Boom Generation, and the Silent generation, respectively, answered in the affirmative

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Problem 1 In a survey of 920 people aged from 18 through 84 years, of whom 80 belonged to the Millenial Generation (18 – 36), 220 belonged to Generation X (37 – 52), 200 belonged to the Baby Boom Generation and the rest belonged to the Silent generation (71+), the following question was asked: Who has slept with a cell phone nearby? 85%, 70%, 50%, and 20% of the people from the Millenial Generation, Generation X, the Baby Boom Generation, and the Silent generation, respectively, answered in the affirmative. (a) (2 pts.) How many people surveyed answered in the affirmative? (b) (3 pts.) If a person in the survey is selected at random and has slept with a cell phone, what is the probability that the person belongs to the Baby Boom generation? (c) (3 pts.) If a person in the survey is selected at random and has not slept with a cell phone, what is the probability that the person belongs to the Millenial Generation? Problem 2 (12 pts.) From a box containing 4 black balls and 2 green balls, 3 balls are drawn in succession, each ball being replaced in the box before the next draw is made. Find the probability mass function of the number of green balls. Problem 4 It is known that 60% of mice inoculated with a serum are protected from a certain disease. If 5 mice are inoculated, find the probability that (a) (4 pts.) none contracts the disease. (b) (4 pts.) fewer than 2 contract the disease. (c) (4 pts.) more than 3 contract the disease. Problem 5 Service calls come to a maintenance center according to a Poisson process, and on average, 2.7 calls are received per minute. Find the probability that (a) (4 pts.) fewer than 2 calls come in any minute. (b) (4 pts.) more than 4 calls come in 3-minute-period. Problem 6 The amount of time that a drive-through bank teller spends on a customer is a random variable with a mean µ=3.2 minutes and a standard deviation σ=1.6 minutes. If a random sample of 64 customers is observed, find the probability that their mean time at the teller’s window is (a) (4 pts.) at most 2.7 minutes. (b) (4 pts.) more than 3.5 minutes. (c) (4 pts.) at least 3.2 minutes but less than 3.4 minutes. Problem 7 The life in hours of a thermocouple used in a furnace is known to be approximately normally distributed, with standard deviation σ=20 hours. A random sample of 15 thermocouples resulted in the following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529. (a) (4 pts.) Is there evidence to support the claim that mean life exceeds 540 hours? Conduct a statistical test with α=0.05. (b) (2 pts.) What is the P-value for this test? Problem 8 (a) (6 pts.) An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 98% confidence interval for the population mean of all bulbs produced by this firm. (b) (4 pts.) How large a sample is needed in (a) if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean? Problem 9 (8 pts.) According to a dietary study, high sodium intake may be related to ulcers, stomach cancer, and migraine headaches. The human requirement for salt is only 220 milligrams per day, which is surpassed in most single servings of ready-to-eat cereals. If a random sample of 20 similar servings of a certain cereal has a mean sodium content of 244 milligrams and a standard deviation of 24.5 milligrams, does this suggest at the 0.05 level of significance that the average sodium content for a single serving of such cereal is greater than 220 milligrams? Assume the distribution of sodium contents to be normal Problem 10 (a) (6 pts.) Compute a 95% confidence interval for the proportion of defective items in a process when it is found that a sample of size 100 yields 8 defectives. (b) (4 pts.) How large a sample is needed in (a) if we wish to be 98% confident that our sample proportion will be within 0.05 of the true proportion defective?