Q1. Suppose x has a distribution with μ = 29 and σ = 22.
(a) If a random sample of size n = 41 is drawn, find μ, σ and P(29 ≤ ≤ 31). (Round σ to two decimal places and the probability to four decimal places.)
(b) If a random sample of size n = 56 is drawn, find μ, σ and P(29 ≤ ≤ 31). (Round σ to two decimal places and the probability to four decimal places.)
Q2. Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean μ = 5.1 and standard deviation σ = 0.6.
(a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.)
(b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.)
(c) Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.)
(d) Convert the z interval, z < -1.44, to an x interval. (Round your answer to one decimal place.)
(e) Convert the z interval, 1.28 < z, to an x interval. (Round your answer to one decimal place.)
(f) Convert the z interval, -2.25 < z < -1.00, to an x interval. (Round your answers to one decimal place.)
(g) If a female had an RBC count of 5.9 or higher, would that be considered unusually high? Explain using z values. Yes. A z score of 1.33 implies that this RBC is unusually high.No. A z score of -1.33 implies that this RBC is unusually low. No. A z score of 1.33 implies that this RBC is normal.
Q3. How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.
75 60 45 50 90 75 30 23 100 110
105 95 105 60 110 120 95 90 60 70
(a) Use a calculator with mean and sample standard deviation keys to find the sample mean price and sample standard deviation s. (Round your answers to two decimal places.)
(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price μ of all summer sleeping bags. (Round your answers to two decimal places.)
Q4. For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
In a survey of 1000 large corporations, 252 said that, given a choice between a job candidate who smokes and an equally qualified nonsmoker, the nonsmoker would get the job.
(a) Let p represent the proportion of all corporations preferring a nonsmoking candidate. Find a point estimate for p. (Round your answer to four decimal places.)
(b) Find a 0.95 confidence interval for p. (Round your answers to three decimal places.)
(c) As a news writer, how would you report the survey results regarding the proportion of corporations that would hire the equally qualified nonsmoker?
What is the margin of error based on a 95% confidence interval? (Round your answer to three decimal places.)
Q5. Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.4 minutes and a standard deviation of 1.4minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)
(a) the response time is between 5 and 10 minutes
(b) the response time is less than 5 minutes
(c) the response time is more than 10 minutes
Q6. A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6 ounces and standard deviation of 0.4 ounce. Examine the figure below and answer the following questions.
(a) Estimate the probability that the machine will overflow an 8-ounce cup. (Round your answer to two decimal places.)
(b) Estimate the probability that the machine will not overflow an 8-ounce cup. (Round your answer to two decimal places.)
(c) The machine has just been loaded with 836 cups. How many of these do you expect will overflow when served?
cups
Q7. Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 2 inches.
(a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)
(b) If a random sample of twenty-eight 18-year-old men is selected, what is the probability that the mean height is between 70 and 72 inches? (Round your answer to four decimal places.)