Let x red blood cell RBC count in millions per cubic millim

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

= 4.2 and standard deviation = 0.2.

(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 8.50 implies that this RBC is unusually high. No. A z score of 8.50 implies that this RBC is unusually low.     No. A z score of 8.50 implies that this RBC is normal.

Solution

a) 4.5<x

or, (4.5-4.2)/0.2<(x-4.2)/0.2   => 1.5<z   [answer]

b) x<4.2 => (x-4.2)/0.2<(4.2-4.2)/0.2 => z<0   [answer]

c) 4<x<5.5   => (4-4.2)/0.2<(x-4.2)/0.2<(5.5-4.2)/0.2 => -1<z<6.5 [answer]

d) z<-1.44 =>(x-4.2)/0.2<-1.44 =>x<3.9 [answer]

e) 1.28<z => 1.28<(x-4.2)/0.2 =>4.5<x   [answer]

f) -2.25<z<-1 => -2.25<(x-4.2)/0.2<-1 =>3.8<x<4    [answer]

g) here x=5.9 hence z score=(5.9-4.2)/0.2=8.5 which is far above than 3 and is very high

hence correct answer is Yes. A z score of 8.50 implies that this RBC is unusually high.