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Random variable and statistical test

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Assume that in healthy American men the level of hemoglobin is normally distributed with mean ?=14 and standard deviation ?=1.1.
a. What is the probability that a healthy man chosen at random will have a hemoglobin of (i) exactly 14, (ii) between 14 and 15, or (iii) over 16.
b. A laboratory wants to check the accuracy of its hemoglobin measurements. It therefore measures the hemoglobin of 400 healthy men, reasoning that the average of these measurements should be very close to the long-run average, which is known to be ?=14. If their method of measurement is accurate and the assumption that ? = 14. And the standard deviation ?=1.1 is also accurate, what is the probability that the average hemoglobin of 400 healthy men will be less than 13.9?
c. Blood is obtained from a single randomly selected healthy man from Papua New Guinea (PNG). The hemoglobin level is 10.7. Do you now believe healthy men in PNG have lower hemoglobin levels?

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Random variables and statistical tests for healthy American men are examined.

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