Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blo
ID: 3227925 • Letter: L
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 = 4.7 and standard deviation = 0.6.
(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 2.00 implies that this RBC is unusually high.No. A z score of 2.00 implies that this RBC is unusually low. No. A z score of 2.00 implies that this RBC is normal.
Explanation / Answer
= 4.7
= 0.6
Z = (X - ) /
a) Z for 4.5 = (4.5 - 4.7) / 0.6 = -0.33
-0.33 < Z
b) Z for 4.2 = (4.2 - 4.7) / 0.6 = -0.83
Z < -0.83
c) Z for 4.0 = (4.0 - 4.7) / 0.6 = -1.17
Z for 5.5 = (5.5 - 4.7) / 0.6 = 1.33
-1.17 < Z < 1.33
d) Z = -1.44
or, (X - 4.7) / 0.6 = -1.44
or, X = -1.44 * 0.6 + 4.7 = 3.84
X < 3.84
e) Z = 1.28
or, (X - 4.7) / 0.6 = 1.28
or, X = 1.28 * 0.6 + 4.7 = 4.77
4.77 < X
f) Z = -2.25
or, (X - 4.7) / 0.6 = -2.25
or, X = -2.25 * 0.6 + 4.7 = 3.35
Z = -1
or, (X - 4.7) / 0.6 = -1
or, X = -1 * 0.6 + 4.7 = 4.1
3.35 < Z < 4.1
g) Z for 5.9 = (5.9 - 4.7) / 0.6 = 2
Option-A) Yes. A z score of 2.00 implies that this RBC is unusually high
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