Answered: Let x = red blood cell (RBC) count in…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 15E: Describe the standard normal distribution. What are its characteristics?

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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 ? = 3.4 and standard deviation ? = 0.5.

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

Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.)
z < ____
Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.)
____ < z < ___

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

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

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

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 5.00 implies that this RBC is unusually high.

No. A z score of −5.00 implies that this RBC is unusually low.

No. A z score of 5.00 implies that this RBC is normal.

The Standard Normal Distribution
(u = 0, o = 1)
%3D
3
-2
3
68% of area
95% of area
99.7% of area

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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