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 *μ* = 6150 and estimated standard deviation *σ*
= 2300. 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 *μ*_{x} = 6150 and
*σ*_{x} = 1150.00.

- The probability distribution of *x* is approximately
normal with *μ*_{x} = 6150 and
*σ*_{x} =
1626.35.

- The probability distribution of *x* is not normal.

- The probability distribution of *x* is approximately
normal with *μ*_{x} = 6150 and
*σ*_{x} = 2300.

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 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.

- 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.

Answer #1

for normal distribution z score =(X-μ)/σx | |

here mean= μ= | 6150 |

std deviation =σ= | 2300 |

a)

probability =P(X<3500)=(Z<(3500-6150)/2300)=P(Z<-1.15)=0.1251 |

b)

- The probability distribution of *x* is approximately
normal with *μ*_{x} = 6150 and
*σ*_{x} = 1626.35.

probability =P(X<3500)=(Z<(3500-6150)/1626.346)=P(Z<-1.63)=0.0516 |

c)

probability =P(X<3500)=(Z<(3500-6150)/1327.906)=P(Z<-2)=0.0228 |

d)

- The probabilities decreased as *n* increased.

- 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.

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