6. 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 80 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean = 80 tons and standard deviation = 0.6 ton. (a) What is the probability that one car chosen at random will have less than 79.5 tons of coal? (Round your answer to four decimal places.)

(b) What is the probability that 33 cars chosen at random will have a mean load weight x of less than 79.5 tons of coal? (Round your answer to four decimal places.)

7. Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 6 inches. (a) What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall? (Round your answer to four decimal places.)

(b) If a random sample of ten 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Round your answer to four decimal places.)

8. Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean = 68 and estimated standard deviation = 20. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)

(b) What is the probability that x < 40? (Round your answer to four decimal places.) (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)

9. Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean = 6550 and estimated standard deviation = 1900. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)

(b) What is the probability of x < 3500? (Round your answer to four decimal places.) (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

10. Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean = 64.0 kg and standard deviation = 8.5 kg. Suppose a doe that weighs less than 55 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.) (b) If the park has about 2500 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) does (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 61 kg. If the average weight is less than 61 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight

x

for a random sample of 40 does is less than 61 kg (assuming a healthy population)? (Round your answer to four decimal places.) (d) Compute the probability that

x

< 65.4 kg for 40 does (assume a healthy population). (Round your answer to four decimal places.)