Vital Statistics: Heights of Men The heights of 18-year-old men are approximately normally distributed, with mean 68 inches and standard a ation 3 inches (based on information from Statistical Abstract of the Uni States, 112th edition). (a) What is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? (b) If a random sample of nine 18-year-old men is selected, what is the probability that the mean height x is between 67 and 69 inches?

Vital Statistics: Heights of Men The heights of 18-year-old men are approximately normally distributed, with mean 68 inches and standard a ation 3 inches (based on information from Statistical Abstract of the Uni States, 112th edition). (a) What is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? (b) If a random sample of nine 18-year-old men is selected, what is the probability that the mean height x is between 67 and 69 inches?

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Concept explainers

2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

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Question

suspect that the loader fnaU Siippct
4.| Vital Statistics: Heights of Men The heights of 18-year-old men are
approximately normally distributed, with mean 68 inches and standard de
ation 3 inches (based on information from Statistical Abstract of the Unit-
States, 112th edition).
(a) What is the probability that an 18-year-old man selected at random is
between 67 and 69 inches tall?
(b) If a random sample of nine 18-year-old men is selected, what is the
probability that the mean height x is between 67 and 69 inches?
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PRACTICE ANOTHER 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 put 82 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean u = 82 tons and standard deviation o = 0.6 ton. (a) What is the probability that one car chosen at random will have less than 81.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 49 cars chosen at random will have a mean load weight x of less than 81.5 tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than 81.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? O Yes O No Suppose the weight of coal in 49 cars selected at random had an average x of less than 81.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? O Yes, the…
Please do both questions thank you
(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.) Standard Error a. o = 30, n = 4 b. o = 30, n = 16 c. o = 30, n = 64