Letxbe a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume thatxhas a distribution that is approximately normal, with mean=6200and estimated standard deviation=2900.A test result ofx<3500is 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,xis less than 3500? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the averagexfor two tests taken about a week apart. What can we say about the probability distribution ofx?

The probability distribution ofxis approximately normal with_x= 6200 and_x= 2050.61.

The probability distribution ofxis not normal.

The probability distribution ofxis approximately normal with_x= 6200 and_x= 1450.00.

The probability distribution ofxis approximately normal with_x= 6200 and_x= 2900.

What is the probability ofx<3500? (Round your answer to four decimal places.)

(c) Repeat part (b) forn= 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 asnincreased?

The probabilities decreased asnincreased.

The probabilities increased asnincreased.

The probabilities stayed the same asnincreased.

If a person hadx<3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

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.

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

Letxbe a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Thenxhas a distribution that is approximately normal with mean=54.0kgand standard deviation=7.2kg.Suppose a doe that weighs less than45kgis 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 about2200does, 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 ofn=45does should be more than51kg. If the average weight is less than51kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weightx

for a random sample of45does is less than51kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability thatx

<55.3kg for45does (assume a healthy population). (Round your answer to four decimal places.)

Suppose park rangers captured, weighed, and released45does in December, and the average weight wasx

=55.3kg.Do you think the doe population is undernourished or not? Explain.

Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.

Since the sample average is below the mean, it is quite likely that the doe population is undernourished.

Since the sample average is above the mean, it is quite likely that the doe population is undernourished.

Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.