Question

# Let x be a random variable that represents white blood cell count per cubic milliliter of...

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 μ = 6950 and estimated standard deviation σ = 2950. 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) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

The probability distribution of x is not normal.

The probability distribution of x is approximately normal with μx = 6950 and σx = 1475.00.

The probability distribution of x is approximately normal with μx = 6950 and σx = 2950.

The probability distribution of x is approximately normal with μx = 6950 and σx = 2085.97.

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.)

(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

The probabilities decreased as n increased.

The probabilities increased as n increased.

The probabilities stayed the same as n increased.

(e) If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

(f) It is known that 85% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 65 new products, find the following probabilities. (Round your answers to four decimal places.)

within 2 years 47 or more fail

within 2 years 58 or fewer fail

within 2 years 15 or more succeed

within 2 years fewer than 10 succeed

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