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 = 4.2 and standard deviation σ = 0.5. (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 3.40 implies that this RBC is unusually high. No. A z score of −3.40 implies that this RBC is unusually low. No. A z score of 3.40 implies that this RBC is normal.

Answer 1

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 = 4.2 and standard deviation σ = 0.5.

i.e.

Then we can write that

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

4.5 < x

or, (4.5 - 4.2) / 0.5 < (x - 4.2) / 0.5

or, 0.6 < z

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

x < 4.2

or, (x - 4.2) / 0.5 < (4.2 - 4.2) / 0.5

or, z < 0

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

4.0 < x < 5.5

or, (4.0 - 4.2) / 0.5 < (x - 4.2) / 0.5 < (5.5 - 4.2) / 0.5

or, -0.4 < z < 2.6

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

z < −1.44

or, (x - 4.2) / 0.5 < -1.44

or, x < (-1.44 * 0.5) + 4.2

or, x < 3.48

or, x<3.5

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

1.28 < z

or, 1.28 < (x - 4.2) / 0.5

or, (1.28 * 0.5) + 4.2 < x

or, 4.84 < x

or, 4.8 < x

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

−2.25 < z < −1.00

or, -2.25 < (x - 4.2) / 0.5 < -1.00

or, (-2.25 * 0.5) + 4.2 < x < (-1.00 * 0.5) + 4.2

or, 3.08 < x < 3.7

or, 3.1 < x < 3.7

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

Here,

so,

or,

Yes. A z score of 3.40 implies that this RBC is unusually high. No. A z score of −3.40 implies that this RBC is unusually low. So, in this case we can conclude that RBC is unusually high.