Let x be a random variable that represents white blood cell count per cubic mill
ID: 3367229 • Letter: L
Question
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 ? = 7650 and estimated standard deviation ? = 2900. 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 approximately normal with ?x = 7650 and ?x = 1450.00. The probability distribution of x is approximately normal with ?x = 7650 and ?x = 2900. The probability distribution of x is not normal. The probability distribution of x is approximately normal with ?x = 7650 and ?x = 2050.61.
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 stayed the same as n increased. The probabilities increased as n increased.
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 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. 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. 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 ? = 7650 and estimated standard deviation ? = 2900. 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 approximately normal with ?x = 7650 and ?x = 1450.00. The probability distribution of x is approximately normal with ?x = 7650 and ?x = 2900. The probability distribution of x is not normal. The probability distribution of x is approximately normal with ?x = 7650 and ?x = 2050.61.
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 stayed the same as n increased. The probabilities increased as n increased.
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 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. 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. 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 ? = 7650 and estimated standard deviation ? = 2900. 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 approximately normal with ?x = 7650 and ?x = 1450.00. The probability distribution of x is approximately normal with ?x = 7650 and ?x = 2900. The probability distribution of x is not normal. The probability distribution of x is approximately normal with ?x = 7650 and ?x = 2050.61.
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 stayed the same as n increased. The probabilities increased as n increased.
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 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. 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.
Explanation / Answer
(a) Probability that, on a single test, X is less than 3500 = P(X < 3500) = P( (X - 7650 / 2900) < ( 3500-7650 /2900 ))
= P(Z < -1.431) = 0.0762
(b) Here n = 2, So mean(x) = 7650 and standard deviation(x) = 2900/?2 = 2050.61.
Suppose a doctor uses the average x for two tests taken about a week apart. The probability distribution of x is approximately normal with ?x = 7650 and ?x = 2050.61.
Probability of x < 3500 = P ( X < 3500 ) = P( (X - 7650 / 2050.61) < (3500 - 7650/ 2050.61 )
= P( Z < -2.0238 ) = 0.0215
(c) Here n = 3, So mean(x) = 7650 and standard deviation(x) = 2900/?3 = 1674.31578.
Suppose a doctor uses the average x for three tests taken about a week apart. The probability distribution of x is approximately normal with ?x = 7650 and ?x = 1674.31578.
Probability of x < 3500 = P ( X < 3500 ) = P( (X - 7650 / 1674.31578) < (3500 - 7650/ 1674.31578 )
= P( Z < -2.4786 ) = 0.0066
(d) The probabilities decreased as n increased.
If a person had x < 3500 based on three tests, Following conclusion would be drawn 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 does not have leukopenia.
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