Question

Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean μ = 5.3 and standard deviation σ = 0.7.

(a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.)
< z

(b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.)
z <

(c) Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.)
< z <

(d) Convert the z interval, z < −1.44, to an x interval. (Round your answer to one decimal place.)
x <

(e) Convert the z interval, 1.28 < z, to an x interval. (Round your answer to one decimal place.)
< x

(f) Convert the z interval, −2.25 < z < −1.00, to an x interval. (Round your answers to one decimal place.)
< x <

(g) If a female had an RBC count of 5.9 or higher, would that be considered unusually high? Explain using z values.

Yes. A z score of 0.86 implies that this RBC is unusually high.No. A z score of −0.86 implies that this RBC is unusually low.    No. A z score of 0.86 implies that this RBC is normal.

Answer 1

Solution :

Given that, X ~ N(5.3, 0.7²)

μ = 5.3 and σ = 0.7

The z-score for a value of X is given as follows :

a) To convert the interval 4.5 < X to a z Interval.

Z score for 4.5 is given by,

Hence,

(4.5 < X) = (-1.14 < Z)

b) To convert the interval X < 4.2 to a z Interval.

Z score for 4.2 is given by,

Hence,

(X < 4.2) = (Z < -1.57)

c) To convert the interval 4.0 < X < 5.5 to a z Interval.

Z score for 4.0 is given by,

Z score for 5.5 is given by,

Hence,

(4.0 < X < 5.5) = (-1.86 < Z < 0.29)

d) To convert the Z < -1.44 to an x interval

The X value for a z score of -1.44 is given by,

Hence,

(Z < -1.44) = (X < 4.3)

e) To convert the 1.28 < Z to an x interval

The X value for a z score of 1.28 is given by,

Hence,

(1.28 < Z) = (6.2 < X)

f) To convert the -2.25 < Z < -1.00 to an x interval

The X value for a z score of -2.25 is given by,

The X value for a z score of -1.00 is given by,

Hence,

(-2.25 < Z < -1.00) = (3.7 < X < 4.6)

g) The z-score for a RBC count of 5.9 is given as follows :

Hence, last option is correct.

No. A z score of 0.86 implies that this RBC is normal.

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