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 = 3.3 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 3.71 implies that this RBC is unusually high. No. A z score of −3.71 implies that this RBC is unusually low. No. A z score of 3.71 implies that this RBC is normal?

Answer 1

Solution:

Given:  x = red blood cell (RBC) count in millions per cubic millimeter of whole blood  has an approximately normal distribution with mean μ = 3.3 and standard deviation σ = 0.7.

Part a) Convert the x interval, 4.5 < x, to a z interval.

Thus z interval is:

1.71 < z

Part b) Convert the x interval, x < 4.2, to a z interval.

Thus z interval is:

z < 1.29

Part c) Convert the x interval, 4.0 < x < 5.5, to a z interval.

Thus z interval is:

1.00 < z < 3.14

Part d) Convert the z interval, z < −1.44, to an x interval.

Use following formula to find x value:

Thus x interval is:

x < 2.3

Part e)  Convert the z interval, 1.28 < z, to an x interval.

Thus x interval is:

4.2 < x

Part f) Convert the z interval, −2.25 < z < −1.00, to an x interval.

and

Thus x interval is:

1.7 < x < 2.6

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

If z score is below -2.00 or above +2.00, then that score is unusually high.

Since z = 3.71 > 2.00, an RBC count of 5.9 or higher, would be considered unusually high.

Thus correct answer is:

Yes. A z score of 3.71 implies that this RBC is unusually high.