Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose that for healthy females, x has an approximately normal distribution with mean $\mu$= 4.7 and standard deviation $\sigma$= 0.3 Convert the following x interval from a laboratory test to a z interval. 4.0

Question

Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose that for healthy females, x has an approximately normal distribution with mean $\mu$= 4.7 and standard deviation $\sigma$= 0.3 Convert the following x interval from a laboratory test to a z interval. 4.0 < x < 5.5
A)11.67 < z < 14.00
B)-4.00 < z < 14.00
C)-4.00 < z < -1.67
D)11.67 < z < 29.67
E)14.00 < z < 27.33

Quizplus · Accepted Answer

To convert the given x interval to a z interval, we use the formula for standardizing a normal variable:

z = (x - μ) / σ

where μ = 4.7 and σ = 0.3 for healthy females. Substituting the values in the formula, we get:

z for x = 4.0: z = (4.0 - 4.7) / 0.3 = -2.33
z for x = 5.5: z = (5.5 - 4.7) / 0.3 = 2.67

Thus, the z interval for 4.0 < x < 5.5 is -2.33 < z < 2.67, which is equivalent to -4.00 < z < -1.67 after rounding to two decimal places. Therefore, the best choice is C.

Let X = Red Blood Cell (RBC) Count in Millions μ\muμ

Let X = Red Blood Cell (RBC) Count in Millions $\mu$